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We present high quality image synthesis results using diffusion probabilistic models, a class of latent variable models inspired by considerations from nonequilibrium thermodynamics. Our best results are obtained by training on a weighted variational bound designed according to a novel connection between diffusion probabilistic models and denoising score matching with Langevin dynamics, and our models naturally admit a progressive lossy decompression scheme that can be interpreted as a generalization of autoregressive decoding. On the unconditional CIFAR10 dataset, we obtain an Inception score of 9.46 and a state-of-the-art FID score of 3.17. On 256x256 LSUN, we obtain sample quality similar to ProgressiveGAN.

Mechanical design and manufacturing workflows conventionally begin with conceptual design, followed by the creation of a computer-aided design (CAD) model and fabrication through material-extrusion (MEX) printing. This process requires converting CAD geometry into machine-readable G-code through slicing and path planning. While each step is well established, dependence on CAD modeling remains a major bottleneck: constructing object-specific 3D geometry is slow and poorly suited to rapid prototyping. Even minor design variations typically necessitate manual updates in CAD software, making iteration time-consuming and difficult to scale. To address this limitation, we introduce Image2Gcode, an end-to-end data-driven framework that bypasses the CAD stage and generates printer-ready G-code directly from images and part drawings. Instead of relying on an explicit 3D model, a hand-drawn or captured 2D image serves as the sole input. The framework first extracts slice-wise structural cues from the image and then employs a denoising diffusion probabilistic model (DDPM) over G-code sequences. Through iterative denoising, the model transforms Gaussian noise into executable print-move trajectories with corresponding extrusion parameters, establishing a direct mapping from visual input to native toolpaths. By producing structured G-code directly from 2D imagery, Image2Gcode eliminates the need for CAD or STL intermediates, lowering the entry barrier for additive manufacturing and accelerating the design-to-fabrication cycle. This approach supports on-demand prototyping from simple sketches or visual references and integrates with upstream 2D-to-3D reconstruction modules to enable an automated pipeline from concept to physical artifact. The result is a flexible, computationally efficient framework that advances accessibility in design iteration, repair workflows, and distributed manufacturing.

Purpose: This study aims to develop and evaluate a three channel denoising diffusion probabilistic model (DDPM) for synthesizing single breast dual view mammograms and to assess the impact of channel representations on image fidelity and cross view consistency. Materials and Methods: A pretrained three channel DDPM, sourced from Hugging Face, was fine tuned on a private dataset of 11020 screening mammograms to generate paired craniocaudal (CC) and mediolateral oblique (MLO) views. Three third channel encodings of the CC and MLO views were evaluated: sum, absolute difference, and zero channel. Each model produced 500 synthetic image pairs. Quantitative assessment involved breast mask segmentation using Intersection over Union (IoU) and Dice Similarity Coefficient (DSC), with distributional comparisons against 2500 real pairs using Earth Movers Distance (EMD) and Kolmogorov Smirnov (KS) tests. Qualitative evaluation included a visual Turing test by a non expert radiologist to assess cross view consistency and artifacts. Results: Synthetic mammograms showed IoU and DSC distributions comparable to real images, with EMD and KS values (0.020 and 0.077 respectively). Models using sum or absolute difference encodings outperformed others in IoU and DSC (p < 0.001), though distributions remained broadly similar. Generated CC and MLO views maintained cross view consistency, with 6 to 8 percent of synthetic images exhibiting artifacts consistent with those in the training data. Conclusion: Three channel DDPMs can generate realistic and anatomically consistent dual view mammograms with promising applications in dataset augmentation.

Denoising Diffusion Probabilistic Models (DDPMs) have established a new state-of-the-art in generative image synthesis, yet their deployment is hindered by significant computational overhead during inference, often requiring up to 1,000 iterative steps. This study presents a rigorous comparative analysis of DDPMs against the emerging Flow Matching (Rectified Flow) paradigm, specifically isolating their geometric and efficiency properties on low-resource hardware. By implementing both frameworks on a shared Time-Conditioned U-Net backbone using the MNIST dataset, we demonstrate that Flow Matching significantly outperforms Diffusion in efficiency. Our geometric analysis reveals that Flow Matching learns a highly rectified transport path (Curvature $\mathcal{C} \approx 1.02$), which is near-optimal, whereas Diffusion trajectories remain stochastic and tortuous ($\mathcal{C} \approx 3.45$). Furthermore, we establish an ``efficiency frontier'' at $N=10$ function evaluations, where Flow Matching retains high fidelity while Diffusion collapses. Finally, we show via numerical sensitivity analysis that the learned vector field is sufficiently linear to render high-order ODE solvers (Runge-Kutta 4) unnecessary, validating the use of lightweight Euler solvers for edge deployment. \textbf{This work concludes that Flow Matching is the superior algorithmic choice for real-time, resource-constrained generative tasks.}

This work introduces InJecteD, a framework for interpreting Denoising Diffusion Probabilistic Models (DDPMs) by analyzing sample trajectories during the denoising process of 2D point cloud generation. We apply this framework to three datasets from the Datasaurus Dozen bullseye, dino, and circle using a simplified DDPM architecture with customizable input and time embeddings. Our approach quantifies trajectory properties, including displacement, velocity, clustering, and drift field dynamics, using statistical metrics such as Wasserstein distance and cosine similarity. By enhancing model transparency, InJecteD supports human AI collaboration by enabling practitioners to debug and refine generative models. Experiments reveal distinct denoising phases: initial noise exploration, rapid shape formation, and final refinement, with dataset-specific behaviors example, bullseyes concentric convergence vs. dinos complex contour formation. We evaluate four model configurations, varying embeddings and noise schedules, demonstrating that Fourier based embeddings improve trajectory stability and reconstruction quality

High-quality audio is essential in a wide range of applications, including online communication, virtual assistants, and the multimedia industry. However, degradation caused by noise, compression, and transmission artifacts remains a major challenge. While diffusion models have proven effective for audio restoration, they typically require significant computational resources and struggle to handle longer missing segments. This study introduces WaveLLDM (Wave Lightweight Latent Diffusion Model), an architecture that integrates an efficient neural audio codec with latent diffusion for audio restoration and denoising. Unlike conventional approaches that operate in the time or spectral domain, WaveLLDM processes audio in a compressed latent space, reducing computational complexity while preserving reconstruction quality. Empirical evaluations on the Voicebank+DEMAND test set demonstrate that WaveLLDM achieves accurate spectral reconstruction with low Log-Spectral Distance (LSD) scores (0.48 to 0.60) and good adaptability to unseen data. However, it still underperforms compared to state-of-the-art methods in terms of perceptual quality and speech clarity, with WB-PESQ scores ranging from 1.62 to 1.71 and STOI scores between 0.76 and 0.78. These limitations are attributed to suboptimal architectural tuning, the absence of fine-tuning, and insufficient training duration. Nevertheless, the flexible architecture that combines a neural audio codec and latent diffusion model provides a strong foundation for future development.

Simulating granular media, using Discrete Element Method is a computationally intensive task. This is especially true during initialization phase, which dominates total simulation time because of large displacements involved and associated kinetic energy. We overcome this bottleneck with a novel generative pipeline based on 3D diffusion models that directly synthesizes arbitrarily large granular assemblies in their final and physically realistic configurations. The approach frames the problem as a 3D generative modeling task, consisting of a two-stage pipeline. First a diffusion model is trained to generate independent 3D voxel grids representing granular media. Second, a 3D inpainting model, adapted from 2D inpainting techniques using masked inputs, stitches these grids together seamlessly, enabling synthesis of large samples with physically realistic structure. The inpainting model explores several masking strategies for the inputs to the underlying UNets by training the network to infer missing portions of voxel grids from a concatenation of noised tensors, masks, and masked tensors as input channels. The model also adapts a 2D repainting technique of re-injecting noise scheduler output with ground truth to provide a strong guidance to the 3D model. This along with weighted losses ensures long-term coherence over generation of masked regions. Both models are trained on the same binarized 3D occupancy grids extracted from small-scale DEM simulations, achieving linear scaling of computational time with respect to sample size. Quantitatively, a 1.2 m long ballasted rail track synthesis equivalent to a 3-hour DEM simulation, was completed under 20 seconds. The generated voxel grids can also be post-processed to extract grain geometries for DEM-compatibility as well, enabling physically coherent, real-time, scalable granular media synthesis for industrial applications.

Despite significant progress in generative modelling, existing diffusion models often struggle to produce anatomically precise female pelvic images, limiting their application in gynaecological imaging, where data scarcity and patient privacy concerns are critical. To overcome these barriers, we introduce a novel diffusion-based framework for uterine MRI synthesis, integrating both unconditional and conditioned Denoising Diffusion Probabilistic Models (DDPMs) and Latent Diffusion Models (LDMs) in 2D and 3D. Our approach generates anatomically coherent, high fidelity synthetic images that closely mimic real scans and provide valuable resources for training robust diagnostic models. We evaluate generative quality using advanced perceptual and distributional metrics, benchmarking against standard reconstruction methods, and demonstrate substantial gains in diagnostic accuracy on a key classification task. A blinded expert evaluation further validates the clinical realism of our synthetic images. We release our models with privacy safeguards and a comprehensive synthetic uterine MRI dataset to support reproducible research and advance equitable AI in gynaecology.

Generative artificial intelligence (AI) is rapidly transforming medical imaging by enabling capabilities such as data synthesis, image enhancement, modality translation, and spatiotemporal modeling. This review presents a comprehensive and forward-looking synthesis of recent advances in generative modeling including generative adversarial networks (GANs), variational autoencoders (VAEs), diffusion models, and emerging multimodal foundation architectures and evaluates their expanding roles across the clinical imaging continuum. We systematically examine how generative AI contributes to key stages of the imaging workflow, from acquisition and reconstruction to cross-modality synthesis, diagnostic support, and treatment planning. Emphasis is placed on both retrospective and prospective clinical scenarios, where generative models help address longstanding challenges such as data scarcity, standardization, and integration across modalities. To promote rigorous benchmarking and translational readiness, we propose a three-tiered evaluation framework encompassing pixel-level fidelity, feature-level realism, and task-level clinical relevance. We also identify critical obstacles to real-world deployment, including generalization under domain shift, hallucination risk, data privacy concerns, and regulatory hurdles. Finally, we explore the convergence of generative AI with large-scale foundation models, highlighting how this synergy may enable the next generation of scalable, reliable, and clinically integrated imaging systems. By charting technical progress and translational pathways, this review aims to guide future research and foster interdisciplinary collaboration at the intersection of AI, medicine, and biomedical engineering.