Related papers: Spectral Diffusion Processes
Can standard continuous-time generative models represent distributions whose support is an extremely sparse, globally constrained discrete set? We study this question using completed Sudoku grids as a controlled testbed, treating them as a…
In this work, we look at Score-based generative models (also called diffusion generative models) from a geometric perspective. From a new view point, we prove that both the forward and backward process of adding noise and generating from…
Diffusion models provide a principled framework for generative modeling via stochastic differential equations and time-reversed dynamics. Extending spectral diffusion approaches to spherical data, however, raises nontrivial geometric and…
Although ensemble generation remains a central challenge in lattice field theory simulations, recent advances in generative modeling may offer a path to accelerated sampling in these contexts. In this work, we implement a framework for…
Euclidean diffusion models have achieved remarkable success in generative modeling across diverse domains, and they have been extended to manifold cases in recent advances. Instead of explicitly utilizing the structure of special manifolds…
This work introduces the generative fractional diffusion model for protein generation (ProT-GFDM), a novel generative framework that employs fractional stochastic dynamics for protein backbone structure modeling. This approach builds on the…
This paper introduces a new probabilistic architecture called Sum-Product Graphical Model (SPGM). SPGMs combine traits from Sum-Product Networks (SPNs) and Graphical Models (GMs): Like SPNs, SPGMs always enable tractable inference using a…
Diffusion models have become a leading framework in generative modeling, yet their theoretical understanding -- especially for high-dimensional data concentrated on low-dimensional structures -- remains incomplete. This paper investigates…
In this work, we address the challenge of multi-task image generation with limited data for denoising diffusion probabilistic models (DDPM), a class of generative models that produce high-quality images by reversing a noisy diffusion…
In this paper, we introduce a new class of score-based generative models (SGMs) designed to handle high-cardinality data distributions by leveraging concepts from mean-field theory. We present mean-field chaos diffusion models (MF-CDMs),…
Diffusion models have had a profound impact on many application areas, including those where data are intrinsically infinite-dimensional, such as images or time series. The standard approach is first to discretize and then to apply…
Score-based (denoising diffusion) generative models have recently gained a lot of success in generating realistic and diverse data. These approaches define a forward diffusion process for transforming data to noise and generate data by…
We show that a Denoising Diffusion Probabalistic Model (DDPM), a class of score-based generative model, can be used to produce realistic mock images that mimic observations of galaxies. Our method is tested with Dark Energy Spectroscopic…
Probabilistic diffusion models have achieved state-of-the-art results for image synthesis, inpainting, and text-to-image tasks. However, they are still in the early stages of generating complex 3D shapes. This work proposes Diffusion-SDF, a…
We introduce Functional Diffusion Processes (FDPs), which generalize score-based diffusion models to infinite-dimensional function spaces. FDPs require a new mathematical framework to describe the forward and backward dynamics, and several…
We introduce a guided stochastic sampling method that augments sampling from diffusion models with physics-based guidance derived from partial differential equation (PDE) residuals and observational constraints, ensuring generated samples…
Score-based diffusion models have emerged as a powerful class of generative methods, achieving state-of-the-art performance across diverse domains. Despite their empirical success, the mathematical foundations of those models remain only…
Physics-inspired Generative Models (GMs), in particular Diffusion Models (DMs) and Poisson Flow Models (PFMs), enhance Bayesian methods and promise great utility in medical imaging. This review examines the transformative role of such…
Since their initial introduction, score-based diffusion models (SDMs) have been successfully applied to solve a variety of linear inverse problems in finite-dimensional vector spaces due to their ability to efficiently approximate the…
Masked generative models (MGMs) have shown impressive generative ability while providing an order of magnitude efficient sampling steps compared to continuous diffusion models. However, MGMs still underperform in image synthesis compared to…