Enhanced Forensic Face Reconstruction: A Conditional U-Net Diffusion Model Approach

Enhanced Forensic Face Reconstruction: A Conditional U-Net Diffusion Model Approach | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Enhanced Forensic Face Reconstruction: A Conditional U-Net Diffusion Model Approach HASAN SABAH AL-MUTTAIRI, Abbas Fadhil Aljuboori, Zahraa Rashid Hameed, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8236322/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Reconstructing realistic faces from forensic sketches is a critical challenge in computer vision, with significant implications for security and forensic applications. This paper introduces an advanced conditional U-Net diffusion model designed to enhance the fidelity and accuracy of facial image reconstruction from sketches. By leveraging a gradual noise reduction process, the model preserves fine structural details more effectively than traditional methods. Using the CUHK dataset, our model achieved a Fréchet Inception Distance of 1.40, a Peak Signal-to-Noise Ratio of 43.15 dB, and a Structural Similarity Index of 99.68%, demonstrating superior performance over DCGAN models. These results set a new standard for high-fidelity forensic face reconstruction, providing a robust tool for criminal identification and media restoration. Artificial Intelligence and Machine Learning Generative Models Conditional Diffusion Forensic Face Reconstruction U-Net cDDPM Sketch to Image Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 1. Introduction After the great progress of technologies in the world, especially in the field of computer vision and data generation these days, diffusion models have emerged as one of the best and most widespread generative models in the field, which depend on their great generative capabilities. These models represent a class of deep generative models that effectively learn the underlying data distribution by reversing a gradual noise propagation process, unlike methods based on GAN networks and automatic regression transformers[ 1 ]. This indicates the excellent performance of diffusion models in generating high-resolution images. The basic principle of diffusion models is based on a solid theoretical framework inspired by non-equilibrium thermodynamics, consisting of two successive processes (1) Forward Process-Diffusion Process: It is a gradual and irreversible Markovian process, in which Gaussian noise is added to the input data as an image in successive time stages (T steps), until the data eventually turns into almost pure Gaussian noise. (2) Reverse diffusion process (Reverse Process): This is the fundamental process that the model learns. A neural network of the U-Net type is often trained to learn the reverse process of noise addition step by step, progressing from a random noise to a sample with a consistent structure that belongs to the original data distribution. What distinguishes diffusion models from previous generative models, such as generative adversarial networks GANs, is their stable approach to training, which avoids the problems of instability and pattern breakdown mode collapse that GANs often face[ 2 ]. The samples they produce are of exceptional quality and accuracy, exceeding those produced by models that rely on Variational Autoencoders (VAEs). Diffusion models have key advantages that set them apart from other models, including training stability, unlike GANs, which can suffer from stabilize and require a balance between the generator and the discriminator[ 3 ]The ability to generate more details, as they can capture intricate details in images and text, resulting in high resolution and high quality outputs, flexibility in use, such as for conditional generation, noise removal, image-to-image translation, and even creating new and innovative content. They also have a strong probabilistic framework, as most models are based on estimating probability distributions, providing a solid mathematical understanding of how data is generated. In this research, we propose to produce realistic human face images from drawn sketches and compare them with DCGAN Models to indicate the efficiency of diffusion Models in producing high-resolution images[ 4 ]. 1.1. Diffusion Models The basic structure of diffusion models is conceptually clear but powerful as shown in Fig. 1 the basic structure of generative models. These models work through two basic processes: the forward noise process and the reverse denoising process. In the forward process, the input image \(\:{\text{x}}_{0}\) is systematically corrupted by adding Gaussian noise via a series of discrete time steps \(\:\:\text{T}\) . This process is designed as a fixed Markov series, where the image in each step \(\:\text{t}\) is derived from the image in the previous step \(\:\text{t}-1\) according to the variance table. By the final time step \(\:\text{T}\) , the image \(\:{\text{x}}_{\text{T}}\:\) is converted into almost pure Gaussian noise. The primary goal of the model is to learn the inverse process[ 5 ]. A neural network (usually a U-Net architecture) is trained to predict the noise removed at each time step, and learn how to effectively reduce image noise. This trained model can then generate new data by starting from random noise \(\:\left({\text{x}}_{T}\right)\) and applying the acquired noise removal steps repeatedly until a coherent image is assembled \(\:\left({\text{x}}_{0}\right)\) . The following sections will discuss in detail the mathematical formula that supports these operations. 1.1.1. Forward Diffusion Process In this multi-step process, Gaussian noise is gradually added to the initial data sample to be transformed into pure noise. In practice, it is worth noting that this was formulated using a Markov chain, which depends only on the state of the previous step. These steps transform the transition of the data distribution process from low entropy to high entropy, which speeds up the original data and makes it undetectable in the noisy sample[ 6 ]. Figure 2 shows the forward process. Given the data point \(\:{x}_{0}\) taken from the real data distribution \(\:\left(x\right)\left({x}_{0}\sim\:q\left(x\right)\right)\) , can define the forward propagation process by adding noise. Specifically, at each step of the Markov chain, we add Gaussian noise with variance \(\:{{\beta\:}}_{t}\:\) to \(\:{x}_{t}-1\) , producing a new latent variable \(\:{x}_{t}\:\) with distribution. This diffusion process can be formulated as follows[ 7 ]: $$\:q\left({x}_{t}|\:{x}_{t}-1\right)=\mathcal{N}\left({x}_{t};\:{\varvec{\mu\:}}_{t}=\sqrt{1-{{\beta\:}}_{t\:}}.\:{\:\varvec{x}}_{t-1}\:,\:{\sum\:}_{t\:}=\:{{\beta\:}}_{t\:}\varvec{I}\right)$$ 1 Considering that we are in a multivariate case, I is the identity matrix, which indicates that each dimension has the same standard deviation βt. Note that q(xt ∣xt − 1) is still a normal distribution, determined by the mean µ and the variance Σ where µt = 1 − βtxt − 1 and Σt = βtI. Σ will always be a diagonal matrix of variances (βt) and therefore, we can move in closed form from input data x0 to xT in a solvable way. Mathematically, this is the posterior probability and is defined as follows: $$\:q\left({x}_{1:T}|\:{x}_{0}\right)=\:\prod\:_{t=1}^{T}q\left({x}_{t}|\:{x}_{t}-1\right)$$ 2 The variance parameter βt can be fixed to a constant or chosen as a schedule during time steps T. In fact, one can define a table of variance, which can be linear, quadratic, cosine, etc. The original DDPM authors used a linear table increasing from β1 = 10 − 4 to βT = 0.02. showed that using a cosine table works best[ 8 ]. 1.1.2. Reverse Diffusion Process This process constitutes the basic generative mechanism for diffusion models. It is responsible for collecting new data by converting random noise into a coherent sample through a series of iterative steps that gradually remove the noise. The reverse process learns to invert forward diffusion by reversing noise steps as shown in Fig. 3 . Each step in the inverse series estimates and subtracts the noise component added during the corresponding forward step[ 9 ]. This is achieved by a neural network (often a U-Net[ 10 ]) trained to predict the noise ε present in the noisy input \(\:{\:\varvec{x}}_{t}\) at time step t. The network prediction \(\:{{\epsilon\:}}_{{\theta\:}}\left({x}_{t},t\right)\) is then used to calculate a slightly noise-free sample \(\:{\:\varvec{x}}_{t-1}\) . This iterative optimization process continues until it reaches the data space at time step 0, producing a new sample that closely matches the distribution of the training data. The inverse process is formally modeled as a Markov chain of learned Gaussian transformations. The neural network determines the parameters of the mean \(\:{{\mu\:}}_{{\theta\:}}\) and (often) the variance \(\:{{\Sigma\:}}_{{\theta\:}}\) of the distribution at each step. The main disadvantage of this approach is its computational cost, as creating a single sample requires several sequential neural network (T) evaluations. This contrasts with GANs, which can produce a sample in a single forward pass through the generator network. The U-Net architecture is particularly suitable for the task of predicting noise in image data due to its ability to capture local and global contextual information through its encryption and decryption architecture while skipping connections[ 10 ]. $$\:q\left(\:{x}_{t}-1|{x}_{t}\right)=\mathcal{N}\left({x}_{t}-1;\:{\varvec{\mu\:}}_{0}\left({x}_{t},t\right)\:,\:{\sum\:}_{0\:}({x}_{t},t\right))$$ 3 1.2. Deep Convolutional Generative Adversarial Network (DCGAN) The DCGAN (deep convolutional generative adversarial network) is a type of GAN that utilizes convolutional neural networks to generate realistic images from random noise[ 11 ]. Proposed it as a radical improvement over GAN models, which suffered from training instability and difficulty generating images. At the same time, CNN architecture profoundly demonstrated a solution to these problems by integrating neural networks. Figure 4 shows that DCGAN consists of two neural networks: (1) A generator that generates images of random noise, whose task is to take the noise vector randomly and convert it into an image that appears to match the truth, and its primary goal is to deceive the discriminator, as it contains fully connected layers, through which random noise is used as input while feeding directly to the convolutional transposed layer, and also Transposed Convolution is used Deconvolution and Batch Normalization to enlarge the dimension vector and use the last layer to help stabilize the training and improve the quality of the final output and finally use the activation function ReLU which approximates the pixel values to the range that corresponds to the values of the processed images, (2) As for the discriminator, its task is to distinguish whether the images are real or fake, and its main goal is to classify correctly, as the CNN network is used with Batch Normalization and the LeakyReLU activation function to prevent fading color gradients, and Sigmoid is used to make the result with a probability between 0 and 1 (real or fake image)[ 12 ]. The two networks trained competitively, as the generator learns to produce increasingly realistic images to deceive the discriminator. DCGAN focuses on speed and sample efficiency, but it also presents some training challenges. Both networks are trained simultaneously, with the discriminator attempting to classify real and fake images correctly, and the generator trying to deceive the discriminator into classifying its fake images as real. Like any other model, the DCGAN network has limitations that govern it, such as resolution, which may be considered low (64 * 64), diversity, as the generator produces a limited set of similar images, and difficulty in training[ 13 ]. 2. Literature Review Koley et al[ 14 ]. To generate sketch-to-image the researchers suggested using Diffusion Models. They employed an abstraction-aware framework utilizing Sketch Adapter, adaptive time-step sampling, and discriminative guidance from a pre-trained FGSBIR model. The dataset involved 12,500 images and 125 categories each image has at least 5 sketches. The training is on the Stable Diffusion v1.5 for 50 epochs using Adam with batch size 8. The results show that even irregular sketches can generate precise images. Guo et al[ 15 ]. To address the shortcomings of current diagram pattern transfer techniques, which often overlook the hierarchical steps of drawing and the details of merging elements, the researchers proposed the Image Diagram Time Generation Pipeline (PSTG). This line simulates the artist's layer-by-layer drawing process, performing generation sequentially, starting with outlines, then facial features, then hair. To achieve this, the researchers designed a composite network structure that combines a global generator responsible for capturing overall features and proportions, and local generators focused on detailed imaging of facial features and hair. The model was trained and evaluated on the public data sets CUFS and CUFSF. The results showed superiority over the total method (Holistic Stylization), with the PSTG method achieving lower scores in the FID (19.85) and LPIPS (0.1798) assessments, and achieving higher scores in the FSIM assessment (0.7402), indicating that the generated images are closer to real images and have less cognitive difference. Zhang et al[ 16 ]. It is suggested to use sketch-guided scene image generation for converting freehand sketches into complex scene images. The researchers used a framework that decomposes the task into object-level cross-domain generation and scene-level image construction. They used a pre-trained diffusion model to convert each object sketch into a separate image, and to preserve foreground fidelity identity embeddings were generated. Scene-level images were constructed by blending foreground objects with background images guided by sketch layouts. Qualitative and quantitative experiments demonstrated that the method outperforms state-of-the-art approaches, maintaining both object consistency and foreground–background fusion. Lu et al[ 17 ]. To address the shortcomings of current GAN-based makeup transfer methods, which often generate soft, high-frequency attributes and inaccurate images, and suffer from training difficulties and model breakdown problems, the researchers introduced the MakeupDiffuse model, a diffusion-based approach. The model is based on the adaptation of a foundational diffusion model pre-trained on large-scale image datasets. Accurate transfer of makeup is achieved through an innovative dual image controller that controls the identity process and adjusts the makeup style. To address the lack of paired data, the researchers included a pre-trained makeup transfer network as a Teacher Module to oversee model training. Furthermore, the researchers proposed a new, objective, and comprehensive quantitative measure of evaluation called Makeup MT-Score. Experiments showed that their model achieves superior performance compared to state-of-the-art methods, achieving the best performance in two sub-indices of the MT-Score scale: Background Consistency (95.58 points) and Facial Persistence (90.34 points), outperforming its closest competitor by about 4.8 points in the latter index. The model also came in second place with a difference of no more than 0.3 points in the "Structure Maintenance" and Quality Goodness indices, and with a difference of less than 0.9 points in the Makeup Style Transferring index. Koley et al[ 18 ] For Zero-Shot Sketch-based Image Retrieval (ZS-SBIR) the researchers suggested using text-to-image diffusion model. They used the intermediate representations of a pre-trained diffusion model, identifying informative UNet layers and enhancing retrieval relevance with visual and textual prompts. Based on three benchmark datasets the method was evaluated: Sketchy (12,500 photos across 125 classes, extended with 60,652 ImageNet photos), QuickDraw (330,000 sketches and 204,000 photos across 110 categories), and TU-Berlin (204,489 photos across 250 categories). The results show significant improvements in state-of-the-art ZS-SBIR methods. Liu et al[ 19 ]. Suggested to use an improved DCGAN for image generation. The researchers enhanced the traditional GAN architecture by redesigning the fully connected layers, using Tanh activation in the generator’s output layer, ReLU in other generator layers, and LeakyReLU in all discriminator layers. Experiments were conducted on the MNIST dataset, evaluating image quality and diversity (ISc). Results demonstrated that the improved DCGAN generated images with 2.02 times higher quality and 1.55 times higher diversity compared to traditional GANs, effectively overcoming low-quality image generation and gradient disappearance issues. Li[ 20 ]. For image generation, the researcher suggested using an improved DCGAN .by redesigning the fully connected layers, using Tanh activation in the generator’s output layer, ReLU in other generator layers, and LeakyReLU in all discriminator layers they improved the traditional GAN architecture. On the MNIST dataset, evaluating image quality and diversity (ISc) Experiments were conducted. The results show that the improved DCGAN generated images with 2.02 times higher in quality and 1.55 times higher diversity compared to traditional GANs by overcoming low-quality image generation and gradient disappearance issues. Ou[ 21 ]. For anime face generation the researcher suggested using DCGAN. The model trained simultaneously on a diverse anime face dataset which comprises a generator with a convolutional transpose structure and a discriminator with a convolutional neural network structure. The dataset contains 63,632 anime face images, preprocessed by scaling, horizontal flipping, and resizing to 64×64 pixels in batches of 32 which were obtained from Kaggle. They analyzed the impact of epoch and batch size on training stability and image quality, and they found that 60 epochs is better than 30 by produced clearer facial features, and a batch size of 32 offered more stable loss curves than 256. The results demonstrated that for generating high-quality anime faces the appropriate hyperparameter selection is crucial. Gao et al[ 22 ]. For semi-supervised SAR automatic target recognition (SAR-ATR) the researchers Suggest using DCGAN. To reduce the impact of incorrectly labeled samples they used two discriminators sharing the same generator, combined with noisy data learning, and to improve recognition performance the model modifies the loss function and uses high-quality generated images for training. Experiments on the MSTAR dataset demonstrated that using generated images enhances accuracy, even with a small number of labeled samples. The researchers analyzed also the impact of the parameter α on performance under varying unlabeled rates, which is showing training results is significantly affects by α. Basori et al[ 23 ]. For COVID-19 chest X-ray image augmentation and detection the researchers proposed to use DCGAN combined with Inception V3 and Xtreme Gradient Boost. To improve dataset quality and enhance prediction performance they used synthetic image generation. Many datasets were used, including the Paul Cohen dataset with normal and pneumonia cases, and an extended version containing COVID-19 samples. The result shows high effectiveness with an accuracy of 98.88%, sensitivity of 99.1%, recall of 98.7%, and F1 score of 98.6%, showing that integrating DCGAN with deep learning and gradient boosting can enhance medical image analysis significantly. Table 1 Literature Review Survey. Author / Year Model Dataset(s) Results Koley et al[ 14 ]. Abstraction-aware Diffusion with Sketch Adapter 12,500 images, 125 classes, sketches (Stable Diffusion v1.5) Precise images even from rough sketches Guo et al[ 15 ] PSTG CUFS, CUFSF It outperforms Holistic SOTA methods in converting an image into a sketch. Zhang et al[ 16 ]. Sketch-guided Scene Image Generation (diffusion + identity embedding) Freehand sketch-to-scene datasets Superior object consistency and foreground–background fusion Lu er at[ 17 ] MakeupDiffuse Extensive datasets (for the foundational diffusion model) as well as the use of a pre-trained makeup transfer network as a teacher unit. Superior performance in transferring makeup. Best on the MT-Score in two indicators: Background Consistency 95.58 points and Facial Persistence 90.34 points. Koley et al[ 18 ]. Text-to-Image Diffusion for ZS-SBIR Sketchy, QuickDraw, TU-Berlin Significant improvement over SOTA in retrieval accuracy Liu et al[ 19 ]. Improved DCGAN (Tanh/ReLU/LeakyReLU modifications) MNIST 2.02× higher quality, 1.55× more diversity Li[ 20 ] DCGAN with Label Smoothing, TTUR, EMD MNIST, Fashion-MNIST Prevented collapse, smoother loss, higher-quality images Ou[ 21 ] DCGAN for Anime Face Generation Kaggle Anime Dataset (63,632 faces) High-quality anime faces; stable with batch size 32 Gao et al [ 22 ]. Semi-supervised DCGAN (two discriminators + generator) MSTAR SAR Dataset Improved recognition accuracy with few labels Basori et al[ 23 ]. DCGAN + Inception V3 + XGBoost Paul Cohen chest X-ray dataset (COVID-19, pneumonia, normal) 98.88% accuracy, 99.1% sensitivity, 98.6% F1 3. Methodology This study aims to build an intelligent model capable of reconstructing the human image by converting hand drawings (Forensic Sketches) into realistic face images. This model is designed for security and investigative applications, where graphics are sometimes the only available source for identifying suspects. Since drawings may be limited in detail or influenced by subjective factors associated with the artist (in this case, a criminal artist), converting them into more realistic, high-resolution images represents a pivotal step in enhancing identity recognition processes. This study focuses on comparing two types of modern generative models: Diffusion models (Diffusion Models): which rely on a gradual process of adding noise to data and then removing it in reverse to reconstruct images, and are among the latest models and most capable of producing high-quality images. Deep Generative Model (DCGAN): It is one of the oldest and most widely used generative models in the field of images, as it relies on the conflict between the generator (Generator) and discriminator (Discriminator) networks to produce new images similar to real images. This comparison comes in response to an urgent need in the criminal field to find more accurate and realistic solutions that can be relied upon to transform sketches into photographs that are close to reality. The success of the identity recognition process depends largely on the system's ability to generate an image that retains the original person's features and is practically usable by investigators and experts. 3.1. Dataset Preparation The proposed model is based on the CUHK face sketch database (CUFS)[ 25 ], an academic database created by the Department of Computer Science at the Chinese University of Hong Kong (CUHK). This rule is specifically designed for research purposes in the field of image conversion between hand drawing (sketch) and a photograph of the person, a field that is a cornerstone of forensic face recognition and computer vision. CUFS is one of the most prominent and well-known databases used worldwide in graphics-to-photos research. the database consists of 1194 pairs of photographs and hand drawings(sketches), prepared with high professionalism, with artists creating sketches based on original photographs of persons. The CUHK's base is characterized by having relatively diverse faces in terms of features and details, while maintaining images with neutral expressions and close imaging conditions, making it particularly suitable for generation and reconstruction tasks generation and reconstruction as shown in Fig. 5 . The images underwent a pre-processing process that included the following: Resize all images to 256×256 pixels to unify inputs. Normalize pixel values to range [− 1,1] to speed up the training process and improve model stability. Divide the data into: 80% for training, 10% for evaluation and validation, 10% for final testing. Increase sample diversity data augmentation to reduce the overfitting problem via techniques such as horizontal flip, and rotation at four angles, and keep the original image. 3.2. Model Implementation The proposed system in this paper is based on the application of the Conditional Denoising Diffusion Probabilistic Model (cDDPM) for conditional noise removal. This model aims to learn an inverse map of the noise addition process, so that the real face image \(\:{x}_{0}\) is gradually reconstructed from random noise \(\:{x}_{T}\) , provided the input diagram c. 3.2.1. Noise Prediction Network The core objective of the Conditional Diffusion Model (cDDPM( is to train a noise prediction network \(\:{{\epsilon\:}}_{{\theta\:}}\left({x}_{t},t,c\right)\) . This network is optimized to predict the noise component ε that corrupted the image \(\:{x}_{t}\) at any given time step t, rather than trying to directly reconstruct the clean image \(\:{x}_{0}\) . This simplifies the learning task, providing superior stability and often resulting in higher perceptual quality in the generated images[ 26 ]. For this crucial function, we use the U-Net architecture. U-Net[ 27 ], [ 28 ] is highly effective for image-to-image translation tasks due to its symmetric encoder-decoder architecture and skip connections, which are vital for capturing both high-level semantic features and preserving low-level spatial detail a necessary for accurate face reconstruction[ 7 ]. The network receives three main inputs: Blurred image ( \(\:{x}_{t})\) : The real face image after adding noise to it at time step t, with three channels to represent an RGB color image (3, 256, 256). Conditional diagram (c): it’s the sketch of the face that provides the basic structure and identity of the person (1, 256, 256). Time step (t): its purpose is to allow the model to learn how to remove noise or to know the current noise level in different amounts depending on the time step in the propagation timeline. To apply the condition (diagram) to the noise removal process, the distorted image \(\:{x}_{t}\) was combined with the diagram c by connecting channels (Channel Concatenation) in the input layer of the U-Net network. As a result of this connection, the U-Net network input layer was modified to receive a 4-channel tensor (Tensor). $$\:\text{Input}=\text{Concatenate}\left({x}_{t},c\right)$$ 4 3.2.2 Forward/Reverse Process The forward process is a Markov Chain that converts a clean real image \(\:{x}_{0}\:\) into pure Gaussian noise \(\:{x}_{t\:}\) gradually and systematically. The total number of time steps for this series is given by T = 200. At each step, a specified amount of Gaussian noise is applied based on a linear variance table. The primary goal of this process is to enable the model to directly estimate the added noise at any random time step (t)[ 7 ]. The background process is the core of the generation and inference stage. This process starts from a tensor containing pure Gaussian noise \(\:{x}_{T}\) , and uses a trained noise guessing network, which is based on the U-Net structure, to guide the noise removal process step by step. In each reverse step, the least noisy image \(\:{x}_{t-1\:}\) is is calculated based on the network's prediction of noise \(\:{\text{ϵ}}_{{\theta\:}}\) in the current noisy image \(\:{x}_{t}\) . This entire process is guided by the condition, which is the face diagram (c), which is directly combined with the distorted image by channel connection. This integration ensures that the noise removal process is not random, but is guided by the structural information and identity provided by the diagram, generating a realistic image identical to the conditional input. 3.3. Training Process The training aims to optimize the network parameters \(\:{\text{ϵ}}_{{\theta\:}}\) to minimize the difference between the actually added random noise \(\:\text{ϵ}\) and that predicted by the network. This is achieved using the mean squared error loss function (MSE), which is a standard function in diffusion models to ensure accurate noise prediction. At each training step, a random sample of clean images \(\:{x}_{0}\) , a random sample of noise \(\:\text{ϵ}\) , and a random time step \(\:t\in\:\left[1,T\right]\:\) are taken. The image \(\:{x}_{t}\:\) is mixed with the diagram (c) to create the conditional input, and then the network is trained to minimize the loss as follows: $$\:\mathcal{L}\left({\theta\:}\right)={E}_{t,{x}_{0},\text{ϵ}}\left[|\text{ϵ}-{\text{ϵ}}_{{\theta\:}}\left({x}_{t},t,c\right){|}^{2}\right]$$ The training process relied on the standard Adam optimizer with an initial learning rate of \(\:{\:10}^{-4}\) , due to its effectiveness and reliability in training deep neural networks. To improve the efficiency of GPU memory utilization and balance the parameter refresh rate, the batch size is set to 8 images. The model was trained for a total of 30,000 steps, a number that ensures good convergence across the expanded data set. To increase the quality and stability of the generated samples, the exponential moving average (EMA) technique was applied, where a second model is slowly updated using the historical average weights of the base model, and this stable model will be used in the final inference stage. 3.4. Evaluation Metrics This section aims to define the metrics that will be used to evaluate the quality of the generated images \(\:{x}_{t\:}\) and compare them to real images. Due to the sensitive nature of converting a diagram into an image (diagram to photograph), metrics that focus on visual similarity and perceptual realism should be used. To evaluate the performance achieved by conditional diffusion models cDDPM and DCGAN models, a comprehensive set of quantitative metrics was used. These metrics are divided into two main categories: measuring perceptual quality and feature similarity, and measuring structural and accuracy. 3.4.1. Quality And Similarity Feature These metrics are used to evaluate how realistic the generated images are and their ability to reflect the true distribution of facial data. Fréchet Inception Distance (FID) : The FID metric is the gold standard for evaluating the quality of generative images. FID works by measuring the distance between the Gaussian distribution of generated image features and the distribution of real image features Ground Truth, within the feature space of an InceptionV3 network pre-trained on a large dataset. A lower FID value reflects a more consistent distribution, demonstrating superior generation quality and higher perceptual realism of images. Kernel Inception Distance (KID) : The KID scale provides an alternative assessment to FID. Instead of measuring the Fréchet distance, it uses the mean squares of distances (MMD) between features. KID is more reliable in small sample size scenarios (Small Sample Sizes), and is used here to provide statistical confirmation of FID results. 3.4.2. Image Structure and Fidelity These metrics focus on measuring the direct similarity between the generated image and the target image at the pixel and structural levels, which is essential for constrained reconstruction tasks. Peak Signal-to-Noise Ratio (PSNR) : PSNR is used as an indication of the structural and direct similarity of the generated image. This scale measures the ratio of maximum signal strength to the strength of corrupted background noise. In the context of image generation, a higher PSNR value indicates a lower absolute pixel-level error, reflecting higher image reconstruction accuracy. Structural Similarity Index Measure (SSIM) : The SSIM scale is a more advanced tool for evaluating image quality because it mimics the human vision system. SSIM measures the structural similarity between two images based on three basic factors: luminance, contrast, and structure. SSIM is more closely related to the quality of human perception than PSNR, and a value closer to 1 indicates an excellent structural match between the generated image and the original image. 3.5. Comparative Analysis To evaluate the effectiveness of conditional diffusion models cDDPM in the sketch-to-image transformation task, a comprehensive quantitative and qualitative comparative analysis will be performed with the Deep Convolutional Generative Adversarial Network DCGAN model. To ensure fair comparison, the conditional DCGAN model will also be trained on the same dataset (CUHK) and using the same data segmentation (80% training, 10% evaluation, 10% testing). The DCGAN model will be adapted to be conditional by integrating the diagram (c) directly with the generator network input Generator by connecting channels, similar to the conditioning mechanism used in the diffusion model. The performance of the two models (cDDPM and DCGAN) will be evaluated via a unified framework that includes quantitative analysis, where results obtained from all evaluation metrics (FID, KID, PSNR, SSIM) are directly compared, as well as qualitative analysis that focuses on displaying visual samples and comparing aspects such as texture realism and skin and hair quality, And the accuracy of the structure to ensure that the features provided by the diagram (c) are maintained. This analysis aims to provide empirical evidence supporting the superiority of diffusion models in terms of perceptual quality and structural similarity, enhancing their reliance in facial forensic recognition applications. 4. Results This section aims to show and evaluate the quantitative and qualitative performance of the proposed conditional diffusion model in the task of generating facial images from sketches. 4.1. Quantitative Evaluation Model performance was comprehensively measured using four standard metrics to evaluate the quality, accuracy, and cognitive realism of generated images. Evaluation was performed on the test set using the correct sampling process (cDDPM/CFG) to ensure results that reflect the actual performance of the model in generation scenarios. The results shown in Table 2 confirm the exceptional performance and superior accuracy of the proposed model. The implications of these results can be summarized in the following points: The PSNR value was 43.15 dB, which is a very high value in the field of generating images from input conditions, indicating that the generated image matches the target image at the pixel level with high accuracy. The SSIM scale reached 0.9968, which reflects an almost complete structural and cognitive match between the generated image and the original image, demonstrating the model's ability to capture structural details and visual patterns rather than just color matching. The FID value 1.40 achieved a level considered excellent for image conversion tasks. This low value indicates that the distribution of generated images is statistically identical to the distribution of real photos in the dataset, which means that the generated images are realistic and difficult to distinguish from real images visually. A KID value close to zero − 0.0011 also reinforces this conclusion, as KID is a more stable measure of comparison between distributions, and its result emphasizes high-quality generation that does not suffer from "collapse patterns" or statistical defects. Table 2 Summary of quantitative evaluation measures for the conditional diffusion model. Metric Description Realized value The perfect direction PSNR Maximum signal-to-noise ratio (dB) 43.15 Higher SSIM Structural similarity index (0–1) 99.68%) − 0.99 (68 Higher (near to 1) FID Fréchet Inception Distance 1.40 Lower KID Kernel Inception Distance -0.0011 Lower (near to 0) Table 3 Summary of Performance and Technology Comparison Table. Model FID (↓) PSNR (↑) SSIM (↑) SR3[ 29 ] 19.2 31.26 0.887 Palette[ 30 ] 4.21 28.43 0.935 IDDPM[ 6 ] 2.90 - - Cold Diffusion[ 31 ] - 32.58 0.973 DCGAN[ 32 ] 37.8 22.15 0.782 LSGAN[ 33 ] 29.4 23.87 0.815 WGAN-GP[ 34 ] 24.8 25.02 0.841 StyleGAN2[ 35 ] 8.32 28.95 0.896 EGAN[36] 19.5 26.41 0.872 Our (cDDPM) 1.40 43.15 0.996 Table 3 shows a quantitative comparison between our proposed model (cDDPM) and the latest methods in the literature, including advanced diffusion models and the GAN family of models. As it clearly shows, our model performs unprecedentedly best across all three metrics. In terms of generative quality and statistical realism, our model records an FID value of 1.40, which is significantly superior to newer diffusion models such as IDDPM[ 6 ] 2.90 and Palette[ 30 ] 4.21, and is strikingly superior to the family of GAN models in which FID values range from 37.8 in the basic DCGAN model[ 32 ] to 8.32 in the advanced StyleGAN2[ 35 ]. This suggests that the statistical distribution of images generated by our model is incomparable in terms of realism and variety. In structural and mathematical accuracy measures, the exceptional values recorded by our model in PSNR (43.15 dB) and SSIM (0.9968) show a clear superiority over all comparative models. Our model outperforms its closest competitors from diffusion models, such as Cold Diffusion[ 31 ] (PSNR 32.58 dB, SSIM 0.973) and SR3[ 29 ] (PSNR 31.26 dB, SSIM 0.887), and also achieves a qualitative leap compared to more advanced GAN models such as StyleGAN2[ 35 ] (PSNR 28.95 dB, SSIM 0.896) and WGAN-GP[ 34 ] (PSNR 25.02 dB, SSIM 0.841). These collective results confirm that our model (cDDPM) achieves the optimal balance between high cognitive quality (reflected by low FID values) and superior mathematical accuracy (reflected by high PSNR and SSIM values). Overall superiority across these disparate metrics highlights the effectiveness of the condition mechanism applied in our model and improvements in the training process, enabling it to overcome the traditional limitations faced by GAN models on the one hand and basic diffusion models on the other. 4.2. Qualitative Results To evaluate the final optical quality and the model's ability to meet the input conditions, a set of generated samples was examined. Figure 6 shows representative examples of the diagram inputs, the corresponding original image, and the image generated by the conditional diffusion model. Figure 6 : Shows samples of the process of converting a sketch of the input condition into a realistic face image. The cDDPM sampling process was used with a routing factor of 6.0. Visual analysis of the results shows the strength of the method used in responding to the condition, the model effectively succeeded in interpreting the abstract lines of the sketch and transforming them into realistic facial features, while maintaining head Pose and details of basic features such as the shape of the eyes, nose and mouth and generating fine details: The model shows superior ability to generate skin texture, hair strands, and silhouette compatible with the general visual conditions of the image. These details contribute significantly to achieving the visual realism confirmed by FID/KID metrics. In addition to achieving visual coherence, unlike other generation models that may fail to integrate elements, the conditional diffusion model generates images with high visual coherence, where all components (background, hair, face) coordinate to form one integrated, high-quality image. These results confirm, both quantitatively and qualitatively, that the applied conditional diffusion model architecture represents a highly effective methodology for converting diagrams into realistic facial images, opening up broad prospects for graphic design and image restoration applications. Based on this quantitatively and qualitatively superior performance, it can be concluded that the proposed conditional diffusion model represents a very effective solution capable of providing photographic quality results in the task of converting a sketch into an image. 5. Conclusion In this study, we successfully investigated the performance of the enhanced conditional diffusion model in the context of sketch-to-image synthesis. We compared its capabilities to the Deep Convolutional Generative Adversarial Network DCGAN model. Experimental evidence overwhelmingly supports the superior performance of the diffusion model, particularly in achieving perceptual accuracy and preserving high-frequency details. Key quantitative achievements highlight this paradigm shift. particularly, the model obtained an unprecedented Fréchet inception distance FID of 1.40, demonstrating that the distribution of generated images is statistically indistinguishable from the real data distribution. This reality is further enhanced by the Kernel inception distance KID of -0.0011. From a pixel-level perspective, the model also excelled, recording a peak signal-to-noise ratio PSNR of 43.15 dB and a structural similarity index SSIM of 0.9968. These metrics demonstrate that the model effectively learns intricate mapping between abstract conditional information (sketch lines) and the complex high-dimensional manifold of real facial images with near-perfect structural coherence. The low in FID, combined with the rise in PSNR/SSIM, underscores the dual strength of the diffusion model: accuracy at the local level and realism at the global level. In summary, this work sets a new and advanced standard for generating realistic faces from forensic sketches. By demonstrating a strong ability to generate highly accurate and perceptually realistic outputs, we advocate the adoption of conditional diffusion models as the leading generative method for high-stakes applications such as criminal identification, portrait generation, and media recovery, where fidelity and authenticity are paramount. Future work will focus on optimizing the model's sampling efficiency to enable real-time applications and expanding the model's robustness to handle complex and unconstrained conditions, including varying illumination, subtle changes in expression, and extreme pose variations. Declarations Conflict of Interest: The authors declare no conflict of interest. Author Contributions: In this study, H.S.K. contributed to making the design and code, and testing the proposed system. A.F.A. supervising and reviewing. M.A.H. contributed the literature review; A.F.A. and Z.R.H. contributed to checking the spelling and checking in terms of content Data Availability: The data presented in this study are available upon request from the corresponding author. References Nichol A et al (2022) GLIDE: Towards Photorealistic Image Generation and Editing with Text-Guided Diffusion Models, Mar. [Online]. Available: http://arxiv.org/abs/2112.10741 Chang Z, Koulieris GA, Chang HJ, Shum HPH On the Design Fundamentals of Diffusion Models: A Survey, May 2025, [Online]. Available: http://arxiv.org/abs/2306.04542 Kairouz P et al Advances and open problems in federated learning. Jun 23 2021 Now Publishers Inc. 10.1561/2200000083 Song Y, Ermon S (2020) Generative Modeling by Estimating Gradients of the Data Distribution, Oct. [Online]. 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Available: http://arxiv.org/abs/1704.00028 Lehtinen J, Aila T NVIDIA, Analyzing and Improving the Image Quality of StyleGAN Tero Karras NVIDIA Samuli Laine NVIDIA Miika Aittala NVIDIA Janne Hellsten NVIDIA. https://doi.org/10.48550/arXiv.1912.04958 Wang Z, She Q, Ward TE Generative Adversarial Networks in Computer Vision: A Survey and Taxonomy, Dec. 2020, [Online]. Available: http://arxiv.org/abs/1906.01529 Additional Declarations The authors declare no competing interests. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-8236322","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":552623918,"identity":"973dcd26-a295-476a-9da1-7a0f6334b12b","order_by":0,"name":"HASAN SABAH 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09:28:17","extension":"png","order_by":22,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":59332,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage9.png","url":"https://assets-eu.researchsquare.com/files/rs-8236322/v1/21cbd9d9f11146fd83373f26.png"},{"id":97461868,"identity":"335562a3-9219-4512-8004-73ab4f941659","added_by":"auto","created_at":"2025-12-04 15:31:33","extension":"xml","order_by":23,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":109280,"visible":true,"origin":"","legend":"","description":"","filename":"rs82363220structuring.xml","url":"https://assets-eu.researchsquare.com/files/rs-8236322/v1/857d94923ff8b8e25977edda.xml"},{"id":97461872,"identity":"bb58ca25-01a7-420a-a284-c7f2efc7ee2c","added_by":"auto","created_at":"2025-12-04 15:31:33","extension":"html","order_by":24,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":123229,"visible":true,"origin":"","legend":"","description":"","filename":"earlyproof.html","url":"https://assets-eu.researchsquare.com/files/rs-8236322/v1/3aae54517841cd3fd41e48f4.html"},{"id":97461842,"identity":"01c29eaf-1565-4383-ba93-3314f54677df","added_by":"auto","created_at":"2025-12-04 15:31:32","extension":"jpg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":89682,"visible":true,"origin":"","legend":"\u003cp\u003eDiffusion Models Overview\u003c/p\u003e","description":"","filename":"1.jpg","url":"https://assets-eu.researchsquare.com/files/rs-8236322/v1/3c6cbfb660dfc68de260a4eb.jpg"},{"id":97667875,"identity":"07d3508d-f714-4c54-ae5e-ef2477b2f78c","added_by":"auto","created_at":"2025-12-08 09:24:25","extension":"jpg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":29443,"visible":true,"origin":"","legend":"\u003cp\u003eForward Diffusion Process.\u003c/p\u003e","description":"","filename":"2.jpg","url":"https://assets-eu.researchsquare.com/files/rs-8236322/v1/ced38c0159d43a1b985bd19d.jpg"},{"id":97461845,"identity":"5eb6313f-32a4-481c-b7ea-fc4d87408bdd","added_by":"auto","created_at":"2025-12-04 15:31:32","extension":"jpg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":35493,"visible":true,"origin":"","legend":"\u003cp\u003eReverse Diffusion Process.\u003c/p\u003e","description":"","filename":"3.jpg","url":"https://assets-eu.researchsquare.com/files/rs-8236322/v1/26589eaf6bed5c1fa9618f8b.jpg"},{"id":97668925,"identity":"91865e80-a1cc-4039-982b-e7ed077c23ec","added_by":"auto","created_at":"2025-12-08 09:26:41","extension":"jpg","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":48946,"visible":true,"origin":"","legend":"\u003cp\u003eDCGAN Architecture Overview\u003c/p\u003e","description":"","filename":"4.jpg","url":"https://assets-eu.researchsquare.com/files/rs-8236322/v1/0a41cd646e276d2d8eab5816.jpg"},{"id":97461848,"identity":"f2ec9b14-29a8-4642-ac4f-baced7ceb4b8","added_by":"auto","created_at":"2025-12-04 15:31:32","extension":"jpg","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":95003,"visible":true,"origin":"","legend":"\u003cp\u003eSample of CUHK Dataset.\u003c/p\u003e","description":"","filename":"5.jpg","url":"https://assets-eu.researchsquare.com/files/rs-8236322/v1/49be932db99375a555f7554f.jpg"},{"id":97667923,"identity":"90176692-5318-4fcf-81a0-1cfc9e73cc5e","added_by":"auto","created_at":"2025-12-08 09:24:29","extension":"jpg","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":288406,"visible":true,"origin":"","legend":"\u003cp\u003eSample of Generated Results.\u003c/p\u003e","description":"","filename":"6.jpg","url":"https://assets-eu.researchsquare.com/files/rs-8236322/v1/80cb6f24d709e1d45ae64573.jpg"},{"id":97677761,"identity":"9a748313-0fd2-4360-bcf5-7fb960e3006f","added_by":"auto","created_at":"2025-12-08 09:54:25","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1415050,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8236322/v1/95136c96-671d-486d-b4ff-b558f22debac.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003e\u003cstrong\u003eEnhanced Forensic Face Reconstruction: A Conditional U-Net Diffusion Model Approach\u003c/strong\u003e\u003c/p\u003e","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eAfter the great progress of technologies in the world, especially in the field of computer vision and data generation these days, diffusion models have emerged as one of the best and most widespread generative models in the field, which depend on their great generative capabilities. These models represent a class of deep generative models that effectively learn the underlying data distribution by reversing a gradual noise propagation process, unlike methods based on GAN networks and automatic regression transformers[\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e]. This indicates the excellent performance of diffusion models in generating high-resolution images. The basic principle of diffusion models is based on a solid theoretical framework inspired by non-equilibrium thermodynamics, consisting of two successive processes (1) Forward Process-Diffusion Process: It is a gradual and irreversible Markovian process, in which Gaussian noise is added to the input data as an image in successive time stages (T steps), until the data eventually turns into almost pure Gaussian noise. (2) Reverse diffusion process (Reverse Process): This is the fundamental process that the model learns. A neural network of the U-Net type is often trained to learn the reverse process of noise addition step by step, progressing from a random noise to a sample with a consistent structure that belongs to the original data distribution. What distinguishes diffusion models from previous generative models, such as generative adversarial networks GANs, is their stable approach to training, which avoids the problems of instability and pattern breakdown mode collapse that GANs often face[\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e]. The samples they produce are of exceptional quality and accuracy, exceeding those produced by models that rely on Variational Autoencoders (VAEs). Diffusion models have key advantages that set them apart from other models, including training stability, unlike GANs, which can suffer from stabilize and require a balance between the generator and the discriminator[\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e]The ability to generate more details, as they can capture intricate details in images and text, resulting in high resolution and high quality outputs, flexibility in use, such as for conditional generation, noise removal, image-to-image translation, and even creating new and innovative content. They also have a strong probabilistic framework, as most models are based on estimating probability distributions, providing a solid mathematical understanding of how data is generated. In this research, we propose to produce realistic human face images from drawn sketches and compare them with DCGAN Models to indicate the efficiency of diffusion Models in producing high-resolution images[\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e].\u003c/p\u003e\u003cdiv id=\"Sec2\" class=\"Section2\"\u003e\u003ch2\u003e1.1. Diffusion Models\u003c/h2\u003e\u003cp\u003eThe basic structure of diffusion models is conceptually clear but powerful as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e the basic structure of generative models. These models work through two basic processes: the forward noise process and the reverse denoising process. In the forward process, the input image \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{x}}_{0}\\)\u003c/span\u003e\u003c/span\u003eis systematically corrupted by adding Gaussian noise via a series of discrete time steps\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\:\\text{T}\\)\u003c/span\u003e\u003c/span\u003e. This process is designed as a fixed Markov series, where the image in each step \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\text{t}\\)\u003c/span\u003e\u003c/span\u003e is derived from the image in the previous step \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\text{t}-1\\)\u003c/span\u003e\u003c/span\u003e according to the variance table. By the final time step \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\text{T}\\)\u003c/span\u003e\u003c/span\u003e, the image \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{x}}_{\\text{T}}\\:\\)\u003c/span\u003e\u003c/span\u003eis converted into almost pure Gaussian noise. The primary goal of the model is to learn the inverse process[\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e]. A neural network (usually a U-Net architecture) is trained to predict the noise removed at each time step, and learn how to effectively reduce image noise. This trained model can then generate new data by starting from random noise \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\left({\\text{x}}_{T}\\right)\\)\u003c/span\u003e\u003c/span\u003e and applying the acquired noise removal steps repeatedly until a coherent image is assembled \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\left({\\text{x}}_{0}\\right)\\)\u003c/span\u003e\u003c/span\u003e. The following sections will discuss in detail the mathematical formula that supports these operations.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cdiv id=\"Sec3\" class=\"Section3\"\u003e\u003ch2\u003e1.1.1. Forward Diffusion Process\u003c/h2\u003e\u003cp\u003eIn this multi-step process, Gaussian noise is gradually added to the initial data sample to be transformed into pure noise. In practice, it is worth noting that this was formulated using a Markov chain, which depends only on the state of the previous step. These steps transform the transition of the data distribution process from low entropy to high entropy, which speeds up the original data and makes it undetectable in the noisy sample[\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e]. Figure\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e shows the forward process.\u003c/p\u003e\u003cp\u003eGiven the data point \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{x}_{0}\\)\u003c/span\u003e\u003c/span\u003e taken from the real data distribution \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\left(x\\right)\\left({x}_{0}\\sim\\:q\\left(x\\right)\\right)\\)\u003c/span\u003e\u003c/span\u003e, can define the forward propagation process by adding noise. Specifically, at each step of the Markov chain, we add Gaussian noise with variance \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{{\\beta\\:}}_{t}\\:\\)\u003c/span\u003e\u003c/span\u003eto \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{x}_{t}-1\\)\u003c/span\u003e\u003c/span\u003e, producing a new latent variable \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{x}_{t}\\:\\)\u003c/span\u003e\u003c/span\u003ewith distribution. This diffusion process can be formulated as follows[\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e]:\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$\\:q\\left({x}_{t}|\\:{x}_{t}-1\\right)=\\mathcal{N}\\left({x}_{t};\\:{\\varvec{\\mu\\:}}_{t}=\\sqrt{1-{{\\beta\\:}}_{t\\:}}.\\:{\\:\\varvec{x}}_{t-1}\\:,\\:{\\sum\\:}_{t\\:}=\\:{{\\beta\\:}}_{t\\:}\\varvec{I}\\right)$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eConsidering that we are in a multivariate case, I is the identity matrix, which indicates that each dimension has the same standard deviation βt. Note that q(xt ∣xt\u0026thinsp;\u0026minus;\u0026thinsp;1) is still a normal distribution, determined by the mean \u0026micro; and the variance Σ where \u0026micro;t\u0026thinsp;=\u0026thinsp;1\u0026thinsp;\u0026minus;\u0026thinsp;βtxt\u0026thinsp;\u0026minus;\u0026thinsp;1 and Σt\u0026thinsp;=\u0026thinsp;βtI. Σ will always be a diagonal matrix of variances (βt) and therefore, we can move in closed form from input data x0 to xT in a solvable way. Mathematically, this is the posterior probability and is defined as follows:\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$$\\:q\\left({x}_{1:T}|\\:{x}_{0}\\right)=\\:\\prod\\:_{t=1}^{T}q\\left({x}_{t}|\\:{x}_{t}-1\\right)$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eThe variance parameter βt can be fixed to a constant or chosen as a schedule during time steps T. In fact, one can define a table of variance, which can be linear, quadratic, cosine, etc. The original DDPM authors used a linear table increasing from β1\u0026thinsp;=\u0026thinsp;10\u0026thinsp;\u0026minus;\u0026thinsp;4 to βT\u0026thinsp;=\u0026thinsp;0.02. showed that using a cosine table works best[\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e].\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec4\" class=\"Section3\"\u003e\u003ch2\u003e1.1.2. Reverse Diffusion Process\u003c/h2\u003e\u003cp\u003eThis process constitutes the basic generative mechanism for diffusion models. It is responsible for collecting new data by converting random noise into a coherent sample through a series of iterative steps that gradually remove the noise. The reverse process learns to invert forward diffusion by reversing noise steps as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e. Each step in the inverse series estimates and subtracts the noise component added during the corresponding forward step[\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e]. This is achieved by a neural network (often a U-Net[\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e]) trained to predict the noise ε present in the noisy input \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\:\\varvec{x}}_{t}\\)\u003c/span\u003e\u003c/span\u003eat time step t. The network prediction \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{{\\epsilon\\:}}_{{\\theta\\:}}\\left({x}_{t},t\\right)\\)\u003c/span\u003e\u003c/span\u003eis then used to calculate a slightly noise-free sample\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\:\\varvec{x}}_{t-1}\\)\u003c/span\u003e\u003c/span\u003e. This iterative optimization process continues until it reaches the data space at time step 0, producing a new sample that closely matches the distribution of the training data. The inverse process is formally modeled as a Markov chain of learned Gaussian transformations. The neural network determines the parameters of the mean \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{{\\mu\\:}}_{{\\theta\\:}}\\)\u003c/span\u003e\u003c/span\u003e and (often) the variance \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{{\\Sigma\\:}}_{{\\theta\\:}}\\)\u003c/span\u003e\u003c/span\u003e of the distribution at each step. The main disadvantage of this approach is its computational cost, as creating a single sample requires several sequential neural network (T) evaluations. This contrasts with GANs, which can produce a sample in a single forward pass through the generator network. The U-Net architecture is particularly suitable for the task of predicting noise in image data due to its ability to capture local and global contextual information through its encryption and decryption architecture while skipping connections[\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e].\u003cdiv id=\"Equ3\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ3\" name=\"EquationSource\"\u003e\n$$\\:q\\left(\\:{x}_{t}-1|{x}_{t}\\right)=\\mathcal{N}\\left({x}_{t}-1;\\:{\\varvec{\\mu\\:}}_{0}\\left({x}_{t},t\\right)\\:,\\:{\\sum\\:}_{0\\:}({x}_{t},t\\right))$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e3\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Sec5\" class=\"Section2\"\u003e\u003ch2\u003e1.2. Deep Convolutional Generative Adversarial Network (DCGAN)\u003c/h2\u003e\u003cp\u003eThe DCGAN (deep convolutional generative adversarial network) is a type of GAN that utilizes convolutional neural networks to generate realistic images from random noise[\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e]. Proposed it as a radical improvement over GAN models, which suffered from training instability and difficulty generating images. At the same time, CNN architecture profoundly demonstrated a solution to these problems by integrating neural networks. Figure\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e shows that DCGAN consists of two neural networks: (1) A generator that generates images of random noise, whose task is to take the noise vector randomly and convert it into an image that appears to match the truth, and its primary goal is to deceive the discriminator, as it contains fully connected layers, through which random noise is used as input while feeding directly to the convolutional transposed layer, and also Transposed Convolution is used Deconvolution and Batch Normalization to enlarge the dimension vector and use the last layer to help stabilize the training and improve the quality of the final output and finally use the activation function ReLU which approximates the pixel values to the range that corresponds to the values of the processed images, (2) As for the discriminator, its task is to distinguish whether the images are real or fake, and its main goal is to classify correctly, as the CNN network is used with Batch Normalization and the LeakyReLU activation function to prevent fading color gradients, and Sigmoid is used to make the result with a probability between 0 and 1 (real or fake image)[\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e]. The two networks trained competitively, as the generator learns to produce increasingly realistic images to deceive the discriminator. DCGAN focuses on speed and sample efficiency, but it also presents some training challenges. Both networks are trained simultaneously, with the discriminator attempting to classify real and fake images correctly, and the generator trying to deceive the discriminator into classifying its fake images as real. Like any other model, the DCGAN network has limitations that govern it, such as resolution, which may be considered low (64 * 64), diversity, as the generator produces a limited set of similar images, and difficulty in training[\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e].\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003c/div\u003e"},{"header":"2. Literature Review","content":"\u003cp\u003eKoley et al[\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e]. To generate sketch-to-image the researchers suggested using Diffusion Models. They employed an abstraction-aware framework utilizing Sketch Adapter, adaptive time-step sampling, and discriminative guidance from a pre-trained FGSBIR model. The dataset involved 12,500 images and 125 categories each image has at least 5 sketches. The training is on the Stable Diffusion v1.5 for 50 epochs using Adam with batch size 8. The results show that even irregular sketches can generate precise images.\u003c/p\u003e\u003cp\u003eGuo et al[\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e]. To address the shortcomings of current diagram pattern transfer techniques, which often overlook the hierarchical steps of drawing and the details of merging elements, the researchers proposed the Image Diagram Time Generation Pipeline (PSTG). This line simulates the artist's layer-by-layer drawing process, performing generation sequentially, starting with outlines, then facial features, then hair. To achieve this, the researchers designed a composite network structure that combines a global generator responsible for capturing overall features and proportions, and local generators focused on detailed imaging of facial features and hair. The model was trained and evaluated on the public data sets CUFS and CUFSF. The results showed superiority over the total method (Holistic Stylization), with the PSTG method achieving lower scores in the FID (19.85) and LPIPS (0.1798) assessments, and achieving higher scores in the FSIM assessment (0.7402), indicating that the generated images are closer to real images and have less cognitive difference.\u003c/p\u003e\u003cp\u003eZhang et al[\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e]. It is suggested to use sketch-guided scene image generation for converting freehand sketches into complex scene images. The researchers used a framework that decomposes the task into object-level cross-domain generation and scene-level image construction. They used a pre-trained diffusion model to convert each object sketch into a separate image, and to preserve foreground fidelity identity embeddings were generated. Scene-level images were constructed by blending foreground objects with background images guided by sketch layouts. Qualitative and quantitative experiments demonstrated that the method outperforms state-of-the-art approaches, maintaining both object consistency and foreground\u0026ndash;background fusion.\u003c/p\u003e\u003cp\u003eLu et al[\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e]. To address the shortcomings of current GAN-based makeup transfer methods, which often generate soft, high-frequency attributes and inaccurate images, and suffer from training difficulties and model breakdown problems, the researchers introduced the MakeupDiffuse model, a diffusion-based approach. The model is based on the adaptation of a foundational diffusion model pre-trained on large-scale image datasets. Accurate transfer of makeup is achieved through an innovative dual image controller that controls the identity process and adjusts the makeup style. To address the lack of paired data, the researchers included a pre-trained makeup transfer network as a Teacher Module to oversee model training. Furthermore, the researchers proposed a new, objective, and comprehensive quantitative measure of evaluation called Makeup MT-Score. Experiments showed that their model achieves superior performance compared to state-of-the-art methods, achieving the best performance in two sub-indices of the MT-Score scale: Background Consistency (95.58 points) and Facial Persistence (90.34 points), outperforming its closest competitor by about 4.8 points in the latter index. The model also came in second place with a difference of no more than 0.3 points in the \"Structure Maintenance\" and Quality Goodness indices, and with a difference of less than 0.9 points in the Makeup Style Transferring index.\u003c/p\u003e\u003cp\u003eKoley et al[\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e] For Zero-Shot Sketch-based Image Retrieval (ZS-SBIR) the researchers suggested using text-to-image diffusion model. They used the intermediate representations of a pre-trained diffusion model, identifying informative UNet layers and enhancing retrieval relevance with visual and textual prompts. Based on three benchmark datasets the method was evaluated: Sketchy (12,500 photos across 125 classes, extended with 60,652 ImageNet photos), QuickDraw (330,000 sketches and 204,000 photos across 110 categories), and TU-Berlin (204,489 photos across 250 categories). The results show significant improvements in state-of-the-art ZS-SBIR methods.\u003c/p\u003e\u003cp\u003eLiu et al[\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e]. Suggested to use an improved DCGAN for image generation. The researchers enhanced the traditional GAN architecture by redesigning the fully connected layers, using Tanh activation in the generator\u0026rsquo;s output layer, ReLU in other generator layers, and LeakyReLU in all discriminator layers. Experiments were conducted on the MNIST dataset, evaluating image quality and diversity (ISc). Results demonstrated that the improved DCGAN generated images with 2.02 times higher quality and 1.55 times higher diversity compared to traditional GANs, effectively overcoming low-quality image generation and gradient disappearance issues.\u003c/p\u003e\u003cp\u003eLi[\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e]. For image generation, the researcher suggested using an improved DCGAN .by redesigning the fully connected layers, using Tanh activation in the generator\u0026rsquo;s output layer, ReLU in other generator layers, and LeakyReLU in all discriminator layers they improved the traditional GAN architecture. On the MNIST dataset, evaluating image quality and diversity (ISc) Experiments were conducted. The results show that the improved DCGAN generated images with 2.02 times higher in quality and 1.55 times higher diversity compared to traditional GANs by overcoming low-quality image generation and gradient disappearance issues.\u003c/p\u003e\u003cp\u003eOu[\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e]. For anime face generation the researcher suggested using DCGAN. The model trained simultaneously on a diverse anime face dataset which comprises a generator with a convolutional transpose structure and a discriminator with a convolutional neural network structure. The dataset contains 63,632 anime face images, preprocessed by scaling, horizontal flipping, and resizing to 64\u0026times;64 pixels in batches of 32 which were obtained from Kaggle. They analyzed the impact of epoch and batch size on training stability and image quality, and they found that 60 epochs is better than 30 by produced clearer facial features, and a batch size of 32 offered more stable loss curves than 256. The results demonstrated that for generating high-quality anime faces the appropriate hyperparameter selection is crucial.\u003c/p\u003e\u003cp\u003eGao et al[\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e]. For semi-supervised SAR automatic target recognition (SAR-ATR) the researchers Suggest using DCGAN. To reduce the impact of incorrectly labeled samples they used two discriminators sharing the same generator, combined with noisy data learning, and to improve recognition performance the model modifies the loss function and uses high-quality generated images for training. Experiments on the MSTAR dataset demonstrated that using generated images enhances accuracy, even with a small number of labeled samples. The researchers analyzed also the impact of the parameter α on performance under varying unlabeled rates, which is showing training results is significantly affects by α.\u003c/p\u003e\u003cp\u003eBasori et al[\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e]. For COVID-19 chest X-ray image augmentation and detection the researchers proposed to use DCGAN combined with Inception V3 and Xtreme Gradient Boost. To improve dataset quality and enhance prediction performance they used synthetic image generation. Many datasets were used, including the Paul Cohen dataset with normal and pneumonia cases, and an extended version containing COVID-19 samples. The result shows high effectiveness with an accuracy of 98.88%, sensitivity of 99.1%, recall of 98.7%, and F1 score of 98.6%, showing that integrating DCGAN with deep learning and gradient boosting can enhance medical image analysis significantly.\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eLiterature Review Survey.\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"4\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eAuthor / Year\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eModel\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eDataset(s)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eResults\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eKoley et al[\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e].\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eAbstraction-aware Diffusion with Sketch Adapter\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e12,500 images, 125 classes, sketches (Stable Diffusion v1.5)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003ePrecise images even from rough sketches\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eGuo et al[\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e]\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003ePSTG\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eCUFS, CUFSF\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eIt outperforms Holistic SOTA methods in converting an image into a sketch.\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eZhang et al[\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e].\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eSketch-guided Scene Image Generation (diffusion\u0026thinsp;+\u0026thinsp;identity embedding)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eFreehand sketch-to-scene datasets\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eSuperior object consistency and foreground\u0026ndash;background fusion\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eLu er at[\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e]\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eMakeupDiffuse\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eExtensive datasets (for the foundational diffusion model) as well as the use of a pre-trained makeup transfer network as a teacher unit.\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eSuperior performance in transferring makeup. Best on the MT-Score in two indicators: Background Consistency 95.58 points and Facial Persistence 90.34 points.\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eKoley et al[\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e].\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eText-to-Image Diffusion for ZS-SBIR\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eSketchy, QuickDraw, TU-Berlin\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eSignificant improvement over SOTA in retrieval accuracy\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eLiu et al[\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e].\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eImproved DCGAN (Tanh/ReLU/LeakyReLU modifications)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eMNIST\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e2.02\u0026times; higher quality, 1.55\u0026times; more diversity\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eLi[\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e]\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eDCGAN with Label Smoothing, TTUR, EMD\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eMNIST, Fashion-MNIST\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003ePrevented collapse, smoother loss, higher-quality images\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eOu[\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e]\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eDCGAN for Anime Face Generation\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eKaggle Anime Dataset (63,632 faces)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eHigh-quality anime faces; stable with batch size 32\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eGao et al [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e].\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eSemi-supervised DCGAN (two discriminators\u0026thinsp;+\u0026thinsp;generator)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eMSTAR SAR Dataset\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eImproved recognition accuracy with few labels\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eBasori et al[\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e].\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eDCGAN\u0026thinsp;+\u0026thinsp;Inception V3\u0026thinsp;+\u0026thinsp;XGBoost\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003ePaul Cohen chest X-ray dataset (COVID-19, pneumonia, normal)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e98.88% accuracy, 99.1% sensitivity, 98.6% F1\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e"},{"header":"3. Methodology","content":"\u003cp\u003eThis study aims to build an intelligent model capable of reconstructing the human image by converting hand drawings (Forensic Sketches) into realistic face images. This model is designed for security and investigative applications, where graphics are sometimes the only available source for identifying suspects. Since drawings may be limited in detail or influenced by subjective factors associated with the artist (in this case, a criminal artist), converting them into more realistic, high-resolution images represents a pivotal step in enhancing identity recognition processes.\u003c/p\u003e\u003cp\u003eThis study focuses on comparing two types of modern generative models:\u003c/p\u003e\u003cp\u003e\u003col style=\"list-style-type:lower-alpha;\"\u003e\u003cspan\u003e\u003cli\u003e\u003cp\u003eDiffusion models (Diffusion Models): which rely on a gradual process of adding noise to data and then removing it in reverse to reconstruct images, and are among the latest models and most capable of producing high-quality images.\u003c/p\u003e\u003c/li\u003e\u003c/span\u003e\u003cspan\u003e\u003cli\u003e\u003cp\u003eDeep Generative Model (DCGAN): It is one of the oldest and most widely used generative models in the field of images, as it relies on the conflict between the generator (Generator) and discriminator (Discriminator) networks to produce new images similar to real images.\u003c/p\u003e\u003c/li\u003e\u003c/span\u003e\u003c/ol\u003e\u003c/p\u003e\u003cp\u003eThis comparison comes in response to an urgent need in the criminal field to find more accurate and realistic solutions that can be relied upon to transform sketches into photographs that are close to reality. The success of the identity recognition process depends largely on the system's ability to generate an image that retains the original person's features and is practically usable by investigators and experts.\u003c/p\u003e\u003cdiv id=\"Sec8\" class=\"Section2\"\u003e\u003ch2\u003e3.1. Dataset Preparation\u003c/h2\u003e\u003cp\u003eThe proposed model is based on the CUHK face sketch database (CUFS)[\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e], an academic database created by the Department of Computer Science at the Chinese University of Hong Kong (CUHK). This rule is specifically designed for research purposes in the field of image conversion between hand drawing (sketch) and a photograph of the person, a field that is a cornerstone of forensic face recognition and computer vision. CUFS is one of the most prominent and well-known databases used worldwide in graphics-to-photos research. the database consists of 1194 pairs of photographs and hand drawings(sketches), prepared with high professionalism, with artists creating sketches based on original photographs of persons. The CUHK's base is characterized by having relatively diverse faces in terms of features and details, while maintaining images with neutral expressions and close imaging conditions, making it particularly suitable for generation and reconstruction tasks generation and reconstruction as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e. The images underwent a pre-processing process that included the following:\u003c/p\u003e\u003cp\u003e\u003col style=\"list-style-type:lower-alpha;\"\u003e\u003cspan\u003e\u003cli\u003e\u003cp\u003eResize all images to 256\u0026times;256 pixels to unify inputs.\u003c/p\u003e\u003c/li\u003e\u003c/span\u003e\u003cspan\u003e\u003cli\u003e\u003cp\u003eNormalize pixel values to range [\u0026minus;\u0026thinsp;1,1] to speed up the training process and improve model stability.\u003c/p\u003e\u003c/li\u003e\u003c/span\u003e\u003cspan\u003e\u003cli\u003e\u003cp\u003eDivide the data into: 80% for training, 10% for evaluation and validation, 10% for final testing.\u003c/p\u003e\u003c/li\u003e\u003c/span\u003e\u003cspan\u003e\u003cli\u003e\u003cp\u003eIncrease sample diversity data augmentation to reduce the overfitting problem via techniques such as horizontal flip, and rotation at four angles, and keep the original image.\u003c/p\u003e\u003c/li\u003e\u003c/span\u003e\u003c/ol\u003e\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec9\" class=\"Section2\"\u003e\u003ch2\u003e3.2. Model Implementation\u003c/h2\u003e\u003cp\u003eThe proposed system in this paper is based on the application of the Conditional Denoising Diffusion Probabilistic Model (cDDPM) for conditional noise removal. This model aims to learn an inverse map of the noise addition process, so that the real face image \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{x}_{0}\\)\u003c/span\u003e\u003c/span\u003e is gradually reconstructed from random noise \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{x}_{T}\\)\u003c/span\u003e\u003c/span\u003e, provided the input diagram c.\u003c/p\u003e\u003cdiv id=\"Sec10\" class=\"Section3\"\u003e\u003ch2\u003e3.2.1. Noise Prediction Network\u003c/h2\u003e\u003cp\u003eThe core objective of the Conditional Diffusion Model (cDDPM( is to train a noise prediction network \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{{\\epsilon\\:}}_{{\\theta\\:}}\\left({x}_{t},t,c\\right)\\)\u003c/span\u003e\u003c/span\u003e. This network is optimized to predict the noise component ε that corrupted the image \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{x}_{t}\\)\u003c/span\u003e\u003c/span\u003e at any given time step t, rather than trying to directly reconstruct the clean image \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{x}_{0}\\)\u003c/span\u003e\u003c/span\u003e. This simplifies the learning task, providing superior stability and often resulting in higher perceptual quality in the generated images[\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e]. For this crucial function, we use the U-Net architecture. U-Net[\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e], [\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e] is highly effective for image-to-image translation tasks due to its symmetric encoder-decoder architecture and skip connections, which are vital for capturing both high-level semantic features and preserving low-level spatial detail a necessary for accurate face reconstruction[\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e]. The network receives three main inputs:\u003c/p\u003e\u003cp\u003e\u003col style=\"list-style-type:lower-alpha;\"\u003e\u003cspan\u003e\u003cli\u003e\u003cp\u003eBlurred image (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{x}_{t})\\)\u003c/span\u003e\u003c/span\u003e: The real face image after adding noise to it at time step t, with three channels to represent an RGB color image (3, 256, 256).\u003c/p\u003e\u003c/li\u003e\u003c/span\u003e\u003cspan\u003e\u003cli\u003e\u003cp\u003eConditional diagram (c): it\u0026rsquo;s the sketch of the face that provides the basic structure and identity of the person (1, 256, 256).\u003c/p\u003e\u003c/li\u003e\u003c/span\u003e\u003cspan\u003e\u003cli\u003e\u003cp\u003eTime step (t): its purpose is to allow the model to learn how to remove noise or to know the current noise level in different amounts depending on the time step in the propagation timeline.\u003c/p\u003e\u003c/li\u003e\u003c/span\u003e\u003c/ol\u003e\u003c/p\u003e\u003cp\u003eTo apply the condition (diagram) to the noise removal process, the distorted image \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{x}_{t}\\)\u003c/span\u003e\u003c/span\u003e was combined with the diagram c by connecting channels (Channel Concatenation) in the input layer of the U-Net network. As a result of this connection, the U-Net network input layer was modified to receive a 4-channel tensor (Tensor).\u003cdiv id=\"Equ4\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ4\" name=\"EquationSource\"\u003e\n$$\\:\\text{Input}=\\text{Concatenate}\\left({x}_{t},c\\right)$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e4\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003e\u003cb\u003e3.2.2 Forward/Reverse Process\u003c/b\u003e\u003c/p\u003e\u003cp\u003eThe forward process is a Markov Chain that converts a clean real image \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{x}_{0}\\:\\)\u003c/span\u003e\u003c/span\u003einto pure Gaussian noise \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{x}_{t\\:}\\)\u003c/span\u003e\u003c/span\u003egradually and systematically. The total number of time steps for this series is given by T\u0026thinsp;=\u0026thinsp;200. At each step, a specified amount of Gaussian noise is applied based on a linear variance table. The primary goal of this process is to enable the model to directly estimate the added noise at any random time step (t)[\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e]. The background process is the core of the generation and inference stage. This process starts from a tensor containing pure Gaussian noise \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{x}_{T}\\)\u003c/span\u003e\u003c/span\u003e, and uses a trained noise guessing network, which is based on the U-Net structure, to guide the noise removal process step by step. In each reverse step, the least noisy image \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{x}_{t-1\\:}\\)\u003c/span\u003e\u003c/span\u003eis is calculated based on the network's prediction of noise \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{ϵ}}_{{\\theta\\:}}\\)\u003c/span\u003e\u003c/span\u003ein the current noisy image \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{x}_{t}\\)\u003c/span\u003e\u003c/span\u003e. This entire process is guided by the condition, which is the face diagram (c), which is directly combined with the distorted image by channel connection. This integration ensures that the noise removal process is not random, but is guided by the structural information and identity provided by the diagram, generating a realistic image identical to the conditional input.\u003c/p\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Sec11\" class=\"Section2\"\u003e\u003ch2\u003e3.3. Training Process\u003c/h2\u003e\u003cp\u003eThe training aims to optimize the network parameters \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{ϵ}}_{{\\theta\\:}}\\)\u003c/span\u003e\u003c/span\u003e to minimize the difference between the actually added random noise \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\text{ϵ}\\)\u003c/span\u003e\u003c/span\u003e and that predicted by the network. This is achieved using the mean squared error loss function (MSE), which is a standard function in diffusion models to ensure accurate noise prediction. At each training step, a random sample of clean images \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{x}_{0}\\)\u003c/span\u003e\u003c/span\u003e, a random sample of noise \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\text{ϵ}\\)\u003c/span\u003e\u003c/span\u003e, and a random time step \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:t\\in\\:\\left[1,T\\right]\\:\\)\u003c/span\u003e\u003c/span\u003eare taken. The image \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{x}_{t}\\:\\)\u003c/span\u003e\u003c/span\u003eis mixed with the diagram (c) to create the conditional input, and then the network is trained to minimize the loss as follows:\u003cdiv id=\"Equa\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equa\" name=\"EquationSource\"\u003e\n$$\\:\\mathcal{L}\\left({\\theta\\:}\\right)={E}_{t,{x}_{0},\\text{ϵ}}\\left[|\\text{ϵ}-{\\text{ϵ}}_{{\\theta\\:}}\\left({x}_{t},t,c\\right){|}^{2}\\right]$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eThe training process relied on the standard Adam optimizer with an initial learning rate of\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\:10}^{-4}\\)\u003c/span\u003e\u003c/span\u003e, due to its effectiveness and reliability in training deep neural networks. To improve the efficiency of GPU memory utilization and balance the parameter refresh rate, the batch size is set to 8 images. The model was trained for a total of 30,000 steps, a number that ensures good convergence across the expanded data set. To increase the quality and stability of the generated samples, the exponential moving average (EMA) technique was applied, where a second model is slowly updated using the historical average weights of the base model, and this stable model will be used in the final inference stage.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec12\" class=\"Section2\"\u003e\u003ch2\u003e3.4. Evaluation Metrics\u003c/h2\u003e\u003cp\u003eThis section aims to define the metrics that will be used to evaluate the quality of the generated images \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{x}_{t\\:}\\)\u003c/span\u003e\u003c/span\u003eand compare them to real images. Due to the sensitive nature of converting a diagram into an image (diagram to photograph), metrics that focus on visual similarity and perceptual realism should be used. To evaluate the performance achieved by conditional diffusion models cDDPM and DCGAN models, a comprehensive set of quantitative metrics was used. These metrics are divided into two main categories: measuring perceptual quality and feature similarity, and measuring structural and accuracy.\u003c/p\u003e\u003cdiv id=\"Sec13\" class=\"Section3\"\u003e\u003ch2\u003e3.4.1. Quality And Similarity Feature\u003c/h2\u003e\u003cp\u003eThese metrics are used to evaluate how realistic the generated images are and their ability to reflect the true distribution of facial data.\u003c/p\u003e\u003cp\u003e\u003col style=\"list-style-type:lower-alpha;\"\u003e\u003cspan\u003e\u003cli\u003e\u003cp\u003e\u003cb\u003eFr\u0026eacute;chet Inception Distance (FID)\u003c/b\u003e: The FID metric is the gold standard for evaluating the quality of generative images. FID works by measuring the distance between the Gaussian distribution of generated image features and the distribution of real image features Ground Truth, within the feature space of an InceptionV3 network pre-trained on a large dataset. A lower FID value reflects a more consistent distribution, demonstrating superior generation quality and higher perceptual realism of images.\u003c/p\u003e\u003c/li\u003e\u003c/span\u003e\u003cspan\u003e\u003cli\u003e\u003cp\u003e\u003cb\u003eKernel Inception Distance (KID)\u003c/b\u003e: The KID scale provides an alternative assessment to FID. Instead of measuring the Fr\u0026eacute;chet distance, it uses the mean squares of distances (MMD) between features. KID is more reliable in small sample size scenarios (Small Sample Sizes), and is used here to provide statistical confirmation of FID results.\u003c/p\u003e\u003c/li\u003e\u003c/span\u003e\u003c/ol\u003e\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec14\" class=\"Section3\"\u003e\u003ch2\u003e3.4.2. Image Structure and Fidelity\u003c/h2\u003e\u003cp\u003eThese metrics focus on measuring the direct similarity between the generated image and the target image at the pixel and structural levels, which is essential for constrained reconstruction tasks.\u003c/p\u003e\u003cp\u003e\u003col style=\"list-style-type:lower-alpha;\"\u003e\u003cspan\u003e\u003cli\u003e\u003cp\u003e\u003cb\u003ePeak Signal-to-Noise Ratio (PSNR)\u003c/b\u003e: PSNR is used as an indication of the structural and direct similarity of the generated image. This scale measures the ratio of maximum signal strength to the strength of corrupted background noise. In the context of image generation, a higher PSNR value indicates a lower absolute pixel-level error, reflecting higher image reconstruction accuracy.\u003c/p\u003e\u003c/li\u003e\u003c/span\u003e\u003cspan\u003e\u003cli\u003e\u003cp\u003e\u003cb\u003eStructural Similarity Index Measure (SSIM)\u003c/b\u003e: The SSIM scale is a more advanced tool for evaluating image quality because it mimics the human vision system. SSIM measures the structural similarity between two images based on three basic factors: luminance, contrast, and structure. SSIM is more closely related to the quality of human perception than PSNR, and a value closer to 1 indicates an excellent structural match between the generated image and the original image.\u003c/p\u003e\u003c/li\u003e\u003c/span\u003e\u003c/ol\u003e\u003c/p\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Sec15\" class=\"Section2\"\u003e\u003ch2\u003e3.5. Comparative Analysis\u003c/h2\u003e\u003cp\u003eTo evaluate the effectiveness of conditional diffusion models cDDPM in the sketch-to-image transformation task, a comprehensive quantitative and qualitative comparative analysis will be performed with the Deep Convolutional Generative Adversarial Network DCGAN model. To ensure fair comparison, the conditional DCGAN model will also be trained on the same dataset (CUHK) and using the same data segmentation (80% training, 10% evaluation, 10% testing). The DCGAN model will be adapted to be conditional by integrating the diagram (c) directly with the generator network input Generator by connecting channels, similar to the conditioning mechanism used in the diffusion model. The performance of the two models (cDDPM and DCGAN) will be evaluated via a unified framework that includes quantitative analysis, where results obtained from all evaluation metrics (FID, KID, PSNR, SSIM) are directly compared, as well as qualitative analysis that focuses on displaying visual samples and comparing aspects such as texture realism and skin and hair quality, And the accuracy of the structure to ensure that the features provided by the diagram (c) are maintained. This analysis aims to provide empirical evidence supporting the superiority of diffusion models in terms of perceptual quality and structural similarity, enhancing their reliance in facial forensic recognition applications.\u003c/p\u003e\u003c/div\u003e"},{"header":"4. Results","content":"\u003cp\u003eThis section aims to show and evaluate the quantitative and qualitative performance of the proposed conditional diffusion model in the task of generating facial images from sketches.\u003c/p\u003e\u003cdiv id=\"Sec17\" class=\"Section2\"\u003e\u003ch2\u003e4.1. Quantitative Evaluation\u003c/h2\u003e\u003cp\u003eModel performance was comprehensively measured using four standard metrics to evaluate the quality, accuracy, and cognitive realism of generated images. Evaluation was performed on the test set using the correct sampling process (cDDPM/CFG) to ensure results that reflect the actual performance of the model in generation scenarios. The results shown in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e confirm the exceptional performance and superior accuracy of the proposed model. The implications of these results can be summarized in the following points:\u003c/p\u003e\u003cp\u003e\u003cul\u003e\u003cli\u003e\u003cp\u003eThe PSNR value was 43.15 dB, which is a very high value in the field of generating images from input conditions, indicating that the generated image matches the target image at the pixel level with high accuracy.\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003eThe SSIM scale reached 0.9968, which reflects an almost complete structural and cognitive match between the generated image and the original image, demonstrating the model's ability to capture structural details and visual patterns rather than just color matching.\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003eThe FID value 1.40 achieved a level considered excellent for image conversion tasks. This low value indicates that the distribution of generated images is statistically identical to the distribution of real photos in the dataset, which means that the generated images are realistic and difficult to distinguish from real images visually.\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003eA KID value close to zero \u0026minus;\u0026thinsp;0.0011 also reinforces this conclusion, as KID is a more stable measure of comparison between distributions, and its result emphasizes high-quality generation that does not suffer from \"collapse patterns\" or statistical defects.\u003c/p\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eSummary of quantitative evaluation measures for the conditional diffusion model.\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"4\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eMetric\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eDescription\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eRealized value\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eThe perfect direction\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003ePSNR\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eMaximum signal-to-noise ratio (dB)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e43.15\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eHigher\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eSSIM\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eStructural similarity index (0\u0026ndash;1)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e99.68%) \u0026minus;\u0026thinsp;0.99 (68\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eHigher (near to 1)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eFID\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eFr\u0026eacute;chet Inception Distance\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e1.40\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eLower\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eKID\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eKernel Inception Distance\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e-0.0011\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eLower (near to 0)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eSummary of Performance and Technology Comparison Table.\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"4\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eModel\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eFID (\u0026darr;)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003ePSNR (\u0026uarr;)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eSSIM (\u0026uarr;)\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eSR3[\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e]\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e19.2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e31.26\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.887\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003ePalette[\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e]\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e4.21\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e28.43\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.935\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eIDDPM[\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e]\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e2.90\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eCold Diffusion[\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e]\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e32.58\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.973\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eDCGAN[\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e]\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e37.8\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e22.15\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.782\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eLSGAN[\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e]\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e29.4\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e23.87\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.815\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eWGAN-GP[\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e]\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e24.8\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e25.02\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.841\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eStyleGAN2[\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e]\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e8.32\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e28.95\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.896\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eEGAN[36]\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e19.5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e26.41\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.872\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eOur (cDDPM)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u003cb\u003e1.40\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e\u003cb\u003e43.15\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e\u003cb\u003e0.996\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e shows a quantitative comparison between our proposed model (cDDPM) and the latest methods in the literature, including advanced diffusion models and the GAN family of models. As it clearly shows, our model performs unprecedentedly best across all three metrics.\u003c/p\u003e\u003cp\u003eIn terms of generative quality and statistical realism, our model records an FID value of 1.40, which is significantly superior to newer diffusion models such as IDDPM[\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e] 2.90 and Palette[\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e] 4.21, and is strikingly superior to the family of GAN models in which FID values range from 37.8 in the basic DCGAN model[\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e] to 8.32 in the advanced StyleGAN2[\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e]. This suggests that the statistical distribution of images generated by our model is incomparable in terms of realism and variety. In structural and mathematical accuracy measures, the exceptional values recorded by our model in PSNR (43.15 dB) and SSIM (0.9968) show a clear superiority over all comparative models. Our model outperforms its closest competitors from diffusion models, such as Cold Diffusion[\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e] (PSNR 32.58 dB, SSIM 0.973) and SR3[\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e] (PSNR 31.26 dB, SSIM 0.887), and also achieves a qualitative leap compared to more advanced GAN models such as StyleGAN2[\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e] (PSNR 28.95 dB, SSIM 0.896) and WGAN-GP[\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e] (PSNR 25.02 dB, SSIM 0.841). These collective results confirm that our model (cDDPM) achieves the optimal balance between high cognitive quality (reflected by low FID values) and superior mathematical accuracy (reflected by high PSNR and SSIM values). Overall superiority across these disparate metrics highlights the effectiveness of the condition mechanism applied in our model and improvements in the training process, enabling it to overcome the traditional limitations faced by GAN models on the one hand and basic diffusion models on the other.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec18\" class=\"Section2\"\u003e\u003ch2\u003e4.2. Qualitative Results\u003c/h2\u003e\u003cp\u003eTo evaluate the final optical quality and the model's ability to meet the input conditions, a set of generated samples was examined. Figure\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e shows representative examples of the diagram inputs, the corresponding original image, and the image generated by the conditional diffusion model.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eFigure \u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e: Shows samples of the process of converting a sketch of the input condition into a realistic face image. The cDDPM sampling process was used with a routing factor of 6.0. Visual analysis of the results shows the strength of the method used in responding to the condition, the model effectively succeeded in interpreting the abstract lines of the sketch and transforming them into realistic facial features, while maintaining head Pose and details of basic features such as the shape of the eyes, nose and mouth and generating fine details: The model shows superior ability to generate skin texture, hair strands, and silhouette compatible with the general visual conditions of the image. These details contribute significantly to achieving the visual realism confirmed by FID/KID metrics. In addition to achieving visual coherence, unlike other generation models that may fail to integrate elements, the conditional diffusion model generates images with high visual coherence, where all components (background, hair, face) coordinate to form one integrated, high-quality image. These results confirm, both quantitatively and qualitatively, that the applied conditional diffusion model architecture represents a highly effective methodology for converting diagrams into realistic facial images, opening up broad prospects for graphic design and image restoration applications. Based on this quantitatively and qualitatively superior performance, it can be concluded that the proposed conditional diffusion model represents a very effective solution capable of providing photographic quality results in the task of converting a sketch into an image.\u003c/p\u003e\u003c/div\u003e"},{"header":"5. Conclusion","content":"\u003cp\u003eIn this study, we successfully investigated the performance of the enhanced conditional diffusion model in the context of sketch-to-image synthesis. We compared its capabilities to the Deep Convolutional Generative Adversarial Network DCGAN model. Experimental evidence overwhelmingly supports the superior performance of the diffusion model, particularly in achieving perceptual accuracy and preserving high-frequency details. Key quantitative achievements highlight this paradigm shift. particularly, the model obtained an unprecedented Fr\u0026eacute;chet inception distance FID of 1.40, demonstrating that the distribution of generated images is statistically indistinguishable from the real data distribution. This reality is further enhanced by the Kernel inception distance KID of -0.0011. From a pixel-level perspective, the model also excelled, recording a peak signal-to-noise ratio PSNR of 43.15 dB and a structural similarity index SSIM of 0.9968. These metrics demonstrate that the model effectively learns intricate mapping between abstract conditional information (sketch lines) and the complex high-dimensional manifold of real facial images with near-perfect structural coherence. The low in FID, combined with the rise in PSNR/SSIM, underscores the dual strength of the diffusion model: accuracy at the local level and realism at the global level. In summary, this work sets a new and advanced standard for generating realistic faces from forensic sketches. By demonstrating a strong ability to generate highly accurate and perceptually realistic outputs, we advocate the adoption of conditional diffusion models as the leading generative method for high-stakes applications such as criminal identification, portrait generation, and media recovery, where fidelity and authenticity are paramount. Future work will focus on optimizing the model's sampling efficiency to enable real-time applications and expanding the model's robustness to handle complex and unconstrained conditions, including varying illumination, subtle changes in expression, and extreme pose variations.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003ch2\u003eConflict of Interest:\u003c/h2\u003e\u003cp\u003eThe authors declare no conflict of interest.\u003c/p\u003e\u003c/p\u003e\u003ch2\u003eAuthor Contributions:\u003c/h2\u003e\u003cp\u003eIn this study, H.S.K. contributed to making the design and code, and testing the proposed system. A.F.A. supervising and reviewing. 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This paper introduces an advanced conditional U-Net diffusion model designed to enhance the fidelity and accuracy of facial image reconstruction from sketches. By leveraging a gradual noise reduction process, the model preserves fine structural details more effectively than traditional methods. Using the CUHK dataset, our model achieved a Fr\u0026eacute;chet Inception Distance of 1.40, a Peak Signal-to-Noise Ratio of 43.15 dB, and a Structural Similarity Index of 99.68%, demonstrating superior performance over DCGAN models. These results set a new standard for high-fidelity forensic face reconstruction, providing a robust tool for criminal identification and media restoration.\u003c/p\u003e","manuscriptTitle":"Enhanced Forensic Face Reconstruction: A Conditional U-Net Diffusion Model Approach","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-12-04 15:31:28","doi":"10.21203/rs.3.rs-8236322/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"4c3f8b3a-caee-47a4-8ec4-00de13d8d4e7","owner":[],"postedDate":"December 4th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":58812580,"name":"Artificial Intelligence and Machine Learning"}],"tags":[],"updatedAt":"2025-12-04T15:31:28+00:00","versionOfRecord":[],"versionCreatedAt":"2025-12-04 15:31:28","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8236322","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8236322","identity":"rs-8236322","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}