Related papers: A Malliavin-Gamma calculus approach to Score Based…
We focus on the fundamental mathematical structure of score-based generative models (SGMs). We first formulate SGMs in terms of the Wasserstein proximal operator (WPO) and demonstrate that, via mean-field games (MFGs), the WPO formulation…
We propose DiffSep, a new single channel source separation method based on score-matching of a stochastic differential equation (SDE). We craft a tailored continuous time diffusion-mixing process starting from the separated sources and…
We present a novel perspective on goal-conditioned reinforcement learning by framing it within the context of denoising diffusion models. Analogous to the diffusion process, where Gaussian noise is used to create random trajectories that…
Score-based generative models exhibit state of the art performance on density estimation and generative modeling tasks. These models typically assume that the data geometry is flat, yet recent extensions have been developed to synthesize…
Diffusion models excel in content generation by implicitly learning the data manifold, yet they lack a practical method to leverage this manifold - unlike other deep generative models equipped with latent spaces. This paper introduces a…
Score-based methods have recently seen increasing popularity in modeling and generation. Methods have been constructed to perform hypothesis testing and change-point detection with score functions, but these methods are in general not as…
We investigate the theoretical properties of general diffusion (interpolation) paths and their Langevin Monte Carlo implementation, referred to as diffusion annealed Langevin Monte Carlo (DALMC), under weak conditions on the data…
Score-based diffusion models have proven effective in image generation and have gained widespread usage; however, the underlying factors contributing to the performance disparity between stochastic and deterministic (i.e., the probability…
We propose a new method for separating superimposed sources using diffusion-based generative models. Our method relies only on separately trained statistical priors of independent sources to establish a new objective function guided by…
We construct surface measures in a Hilbert space endowed with a probability measure $\nu$. The theory fits for invariant measures of some stochastic partial differential equations such as Burgers and reaction--diffusion equations. Other…
We derive a general change of variables formula for score functions, showing that for a smooth, invertible transformation $\mathbf{y} = \phi(\mathbf{x})$, the transformed score function $\nabla_{\mathbf{y}} \log q(\mathbf{y})$ can be…
Generative diffusion models apply the concept of Langevin dynamics in physics to machine leaning, attracting a lot of interests from engineering, statistics and physics, but a complete picture about inherent mechanisms is still lacking. In…
Diffusion models generate high-dimensional data with remarkable quality, yet how their training efficiently learns the score function, bypassing the curse of dimensionality when data is supported on low-dimensional manifolds, remains…
Diffusion models are a state-of-the-art generative modeling framework that transform noise to images via Langevin sampling, guided by the score, which is the gradient of the logarithm of the data distribution. Recent works have shown…
In this work, we consider the numerical recovery of a spatially dependent diffusion coefficient in a subdiffusion model from distributed observations. The subdiffusion model involves a Caputo fractional derivative of order $\alpha\in(0,1)$…
The stochastic reaction-diffusion model driven by a multiplicative noise is examined. We construct the gradient discretisation method (GDM), an abstract framework combining several numerical method families. The paper provides the…
The success of denoising diffusion models raises important questions regarding their generalisation behaviour, particularly in high-dimensional settings. Notably, it has been shown that when training and sampling are performed perfectly,…
Generative models based on diffusion have become the state of the art in the last few years, notably for image generation. Here, we analyse them in the high-dimensional limit, where data are formed by a very large number of variables. We…
Diffusion models are often introduced from multiple perspectives, such as VAEs, score matching, or flow matching, accompanied by dense and technically demanding mathematics that can be difficult for beginners to grasp. One classic question…
Diffusion models are gaining widespread use in cutting-edge image, video, and audio generation. Score-based diffusion models stand out among these methods, necessitating the estimation of score function of the input data distribution. In…