ABSTRACT Discrete diffusion models are a powerful class of generative models with strong performance across many domains. For efficiency, however, discrete diffusion typically parameterizes the generative (reverse) process with factorized distributions, which makes it difficult for the model to learn the target process in a small number of steps and necessitates a long, computationally expensive sampling procedure. To reduce the gap between the target and model distributions and enable few-step generation, we propose Forward-Learned Discrete Diffusion (FLDD), which introduces discrete diffusion with a learnable forward (noising) process. Rather than fixing a Markovian forward chain, we adopt a non-Markovian formulation with learnable marginal and posterior distributions. This allows the generative process to remain factorized while matching the target defined by the noising process. We train all parameters end-to-end under the standard variational objective. Experiments on various benchmarks show that, for a given number of sampling steps, our approach produces a higher quality samples than conventional discrete diffusion models using the same reverse parameterization. 1 INTRODUCTION In the last years, diffusion models have demonstrated strong performance across many continuous (Hoogeboom et al., 2024) and discrete (Lou et al.) domains . Recent work has shown that distillation approaches and advanced training techniques allow learning a few-step (Salimans et al., 2024), or sometimes even a single-step, generative (Xu et al., 2025) procedure in the continuous domain.

Deep learning-based image stitching pipelines are typically divided into three cascading stages: registration, fusion, and rectangling. Each stage requires its own network training and is tightly coupled to the others, leading to error propagation and posing significant challenges to parameter tuning and system stability. This paper proposes the Simple and Robust Stitcher (SRStitcher), which revolutionizes the image stitching pipeline by simplifying the fusion and rectangling stages into a unified inpainting model, requiring no model training or fine-tuning. We reformulate the problem definitions of the fusion and rectangling stages and demonstrate that they can be effectively integrated into an inpainting task. Furthermore, we design the weighted masks to guide the reverse process in a pre-trained largescale diffusion model, implementing this integrated inpainting task in a single inference. Through extensive experimentation, we verify the interpretability and generalization capabilities of this unified model, demonstrating that SRStitcher outperforms state-of-the-art methods in both performance and stability.

Denoising Diffusion Probabilistic Models (DDPMs) provide the foundation for the recent breakthroughs in generative modeling. Their Markovian structure makes it difficult to define DDPMs with distributions other than Gaussian or discrete. In this paper, we introduce Star-Shaped DDPM (SS-DDPM). Its star-shaped diffusion process allows us to bypass the need to define the transition probabilities or compute posteriors. We establish duality between star-shaped and specific Markovian diffusions for the exponential family of distributions and derive efficient algorithms for training and sampling from SS-DDPMs. In the case of Gaussian distributions, SS-DDPM is equivalent to DDPM. However, SS-DDPMs provide a simple recipe for designing diffusion models with distributions such as Beta, von Mises-Fisher, Dirichlet, Wishart and others, which can be especially useful when data lies on a constrained manifold. We evaluate the model in different settings and find it competitive even on image data, where Beta SS-DDPM achieves results comparable to a Gaussian DDPM.

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.

To address the error propagation problem, we identify image fusion as the key point for improvement.

Diffusion models have significantly advanced the field of generative modeling.