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.

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.

In denoising diffusion probabilistic models (DDPMs), the learned noise predictor $ ε_θ ( {\bf x}_t , t)$ is trained to approximate the forward-process noise $ε_t$. The equality $\nabla_{{\bf x}_t} \log q({\bf x}_t) = -\frac 1 {\sqrt {1- {\bar α}_t} } ε_θ ( {\bf x}_t , t)$ plays a fundamental role in both theoretical analyses and algorithmic design, and thus is frequently employed across diffusion-based generative models. In this paper, an explicit formulation of $ ε_θ ( {\bf x}_t , t)$ in terms of the forward-process noise $ε_t$ is derived. This result show how the forward-process noise $ε_t$ contributes to the learned predictor $ ε_θ ( {\bf x}_t , t)$. Furthermore, based on this formulation, we present a novel and mathematically rigorous proof of the fundamental equality above, clarifying its origin and providing new theoretical insight into the structure of diffusion models.

Recently, research on denoising diffusion models has expanded its application to the field of image restoration. Traditional diffusion-based image restoration methods utilize degraded images as conditional input to effectively guide the reverse generation process, without modifying the original denoising diffusion process. However, since the degraded images already include low-frequency information, starting from Gaussian white noise will result in increased sampling steps. We propose Resfusion, a general framework that incorporates the residual term into the diffusion forward process, starting the reverse process directly from the noisy degraded images. The form of our inference process is consistent with the DDPM.

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.

--Efficient compression of low-bit-rate point clouds is critical for bandwidth-constrained applications. However, existing techniques mainly focus on high-fidelity reconstruction, requiring many bits for compression. This paper proposes a "Denoising Diffusion Probabilistic Model" (DDPM) architecture for point cloud compression (DDPM-PCC) at low bit-rates. A PointNet encoder produces the condition vector for the generation, which is then quantized via a learnable vector quantizer . This configuration allows to achieve a low bitrates while preserving quality. Experiments on ShapeNet and ModelNet40 show improved rate-distortion at low rates compared to standardized and state-of-the-art approaches.