Related papers: Analysis of Diffusion Models for Manifold Data
Generative modeling is typically framed as learning mapping rules, but from an observer's perspective without access to these rules, the task becomes disentangling the geometric support from the probability distribution. We propose that…
Score-based diffusion models are a class of generative models whose dynamics is described by stochastic differential equations that map noise into data. While recent works have started to lay down a theoretical foundation for these models,…
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…
Diffusion based generative models have achieved unprecedented fidelity in synthesizing high dimensional data, yet the theoretical mechanisms governing multimodal generation remain poorly understood. Here, we present a theoretical framework…
Denoising diffusion models have become ubiquitous for generative modeling. The core idea is to transport the data distribution to a Gaussian by using a diffusion. Approximate samples from the data distribution are then obtained by…
Deep generative models produce data according to a learned representation, e.g. diffusion models, through a process of approximation computing possible samples. Approximation can be understood as reconstruction and the large datasets used…
Score-based diffusion models are a powerful class of generative models, but their practical use often depends on training neural networks to approximate the score function. Training-free diffusion models provide an attractive alternative by…
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…
Diffusion models have emerged as powerful generative frameworks by progressively adding noise to data through a forward process and then reversing this process to generate realistic samples. While these models have achieved strong…
Generative models have enjoyed widespread success in a variety of applications. However, they encounter inherent mathematical limitations in modeling distributions where samples are constrained by equalities, as is frequently the setting in…
Diffusion generative models unlock new possibilities for inverse problems as they allow for the incorporation of strong empirical priors in scientific inference. Recently, diffusion models are repurposed for solving inverse problems using…
Generative diffusions are a powerful class of Monte Carlo samplers that leverage bridging Markov processes to approximate complex, high-dimensional distributions, such as those found in image processing and language models. Despite their…
Score-based diffusion models generate samples from a complex underlying data distribution by time-reversal of a diffusion process and represent the state-of-the-art in many generative AI applications. Here, I show how a generative diffusion…
We study the memorization and generalization capabilities of Diffusion Models (DMs) when data lies on a structured latent manifold. Specifically, we consider a set of $P$ data points in $N$ dimensions confined to a latent subspace of…
Cloth manipulation is challenging due to its highly complex dynamics, near-infinite degrees of freedom, and frequent self-occlusions, which complicate both state estimation and dynamics modeling. Inspired by recent advances in generative…
A central problem in machine learning involves modeling complex data-sets using highly flexible families of probability distributions in which learning, sampling, inference, and evaluation are still analytically or computationally…
Diffusion models, a family of generative models based on deep learning, have become increasingly prominent in cutting-edge machine learning research. With a distinguished performance in generating samples that resemble the observed data,…
Discrete-time diffusion-based generative models and score matching methods have shown promising results in modeling high-dimensional image data. Recently, Song et al. (2021) show that diffusion processes that transform data into noise can…
We study a data-dependent notion of diffusion-model generalization: when a model does not memorize the training set, where do its generated samples go relative to the geometry induced by the data? To answer this, we introduce a…
In recent years, generative diffusion models have achieved a rapid paradigm shift in deep generative models by showing groundbreaking performance across various applications. Meanwhile, structured data, encompassing tabular and time series…