Related papers: Riemannian Score-Based Generative Modelling
Score-based diffusion models generate new samples by learning the score function associated with a diffusion process. While the effectiveness of these models can be theoretically explained using differential equations related to the…
We present SURE-Score: an approach for learning score-based generative models using training samples corrupted by additive Gaussian noise. When a large training set of clean samples is available, solving inverse problems via score-based…
We propose a framework to perform Bayesian inference using conditional score-based diffusion models to solve a class of inverse problems in mechanics involving the inference of a specimen's spatially varying material properties from noisy…
Estimating means on Riemannian manifolds is generally computationally expensive because the Riemannian distance function is not known in closed-form for most manifolds. To overcome this, we show that Riemannian diffusion means can be…
Dynamic magnetic resonance image reconstruction from incomplete k-space data has generated great research interest due to its capability to reduce scan time. Never-theless, the reconstruction problem is still challenging due to its…
In this paper, we propose a general methodology for sampling from un-normalized densities defined on Riemannian manifolds, with a particular focus on multi-modal targets that remain challenging for existing sampling methods. Inspired by the…
We introduce Spatial Reasoning Models (SRMs), a framework to perform reasoning over sets of continuous variables via denoising generative models. SRMs infer continuous representations on a set of unobserved variables, given observations on…
This work explores the theoretical and practical foundations of denoising diffusion probabilistic models (DDPMs) and score-based generative models, which leverage stochastic processes and Brownian motion to model complex data distributions.…
Graph diffusion models have made significant progress in learning structured graph data and have demonstrated strong potential for predictive tasks. Existing approaches typically embed node, edge, and graph-level features into a unified…
In this paper, we investigate the latent geometry of generative diffusion models under the manifold hypothesis. For this purpose, we analyze the spectrum of eigenvalues (and singular values) of the Jacobian of the score function, whose…
Denoising diffusion models have proven to be a flexible and effective paradigm for generative modelling. Their recent extension to infinite dimensional Euclidean spaces has allowed for the modelling of stochastic processes. However, many…
While the manifold hypothesis is widely adopted in modern machine learning, complex data is often better modeled as stratified spaces -- unions of manifolds (strata) of varying dimensions. Stratified learning is challenging due to varying…
This study investigates the dynamics of Score-based Generative Models (SGMs) by treating the score estimation error as a stochastic source driving the Fokker-Planck equation. Departing from particle-centric SDE analyses, we employ an SPDE…
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 a new score-based model with one-step sampling. Previously, score-based models were burdened with heavy computations due to iterative sampling. For substituting the iterative process, we train a standalone generator to compress…
Local climate information is crucial for impact assessment and decision-making, yet coarse global climate simulations cannot capture small-scale phenomena. Current statistical downscaling methods infer these phenomena as temporally…
We survey continuous-time generative modeling methods based on transporting a simple reference distribution to a data distribution via stochastic or deterministic dynamics. We present a unified framework in which diffusion models,…
Score-based diffusion models (SBDM) have recently emerged as state-of-the-art approaches for image generation. Existing SBDMs are typically formulated in a finite-dimensional setting, where images are considered as tensors of finite size.…
Score-based diffusion models have emerged as one of the most promising frameworks for deep generative modelling. In this work we conduct a systematic comparison and theoretical analysis of different approaches to learning conditional…
Recent advances in generative models have made exploring design spaces easier for de novo molecule generation. However, popular generative models like GANs and normalizing flows face challenges such as training instabilities due to…