Related papers: Categorical SDEs with Simplex Diffusion
Typical generative diffusion models rely on a Gaussian diffusion process for training the backward transformations, which can then be used to generate samples from Gaussian noise. However, real world data often takes place in discrete-state…
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.…
Diffusion-based generative models learn to iteratively transfer unstructured noise to a complex target distribution as opposed to Generative Adversarial Networks (GANs) or the decoder of Variational Autoencoders (VAEs) which produce samples…
Diffusion models have emerged as a dominant framework for generative modeling, but their mathematical foundations are often presented separately through diffusion probabilistic models, score-based modeling, stochastic differential…
The proposed BSDE-based diffusion model represents a novel approach to diffusion modeling, which extends the application of stochastic differential equations (SDEs) in machine learning. Unlike traditional SDE-based diffusion models, our…
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 introduce a novel class of score-based diffusion processes that operate directly in the representation space of Lie groups. Leveraging the framework of Generalized Score Matching, we derive a class of Langevin dynamics that decomposes as…
Diffusion or score-based models recently showed high performance in image generation. They rely on a forward and a backward stochastic differential equations (SDE). The sampling of a data distribution is achieved by numerically solving the…
Diffusion models have emerged as a promising alternative to autoregressive models in modeling discrete categorical data. However, diffusion models that directly work on discrete data space fail to fully exploit the power of iterative…
We study a discrete denoising diffusion framework that integrates a sample-efficient estimator of single-site conditionals with round-robin noising and denoising dynamics for generative modeling over discrete state spaces. Rather than…
Score-based diffusion models provide a powerful way to model images using the gradient of the data distribution. Leveraging the learned score function as a prior, here we introduce a way to sample data from a conditional distribution given…
We develop a class of non-Gaussian translation processes that extend classical stochastic differential equations (SDEs) by prescribing arbitrary absolutely continuous marginal distributions. Our approach uses a copula-based transformation…
Denoising diffusion models are a novel class of generative models that have recently become extremely popular in machine learning. In this paper, we describe how such ideas can also be used to sample from posterior distributions and, more…
Discrete diffusion models are a class of generative models that produce samples from an approximated data distribution within a discrete state space. Often, there is a need to target specific regions of the data distribution. Current…
Diffusion models have shown remarkable progress in various generative tasks such as image and video generation. This paper studies the problem of leveraging pretrained diffusion models for performing discriminative tasks. Specifically, we…
A prominent family of methods for learning data distributions relies on density ratio estimation (DRE), where a model is trained to $\textit{classify}$ between data samples and samples from some reference distribution. DRE-based models can…
To model discrete sequences such as DNA, proteins, and language using diffusion, practitioners must choose between three major methods: diffusion in discrete space, Gaussian diffusion in Euclidean space, or diffusion on the simplex. Despite…
Denoising diffusion models have spurred significant gains in density modeling and image generation, precipitating an industrial revolution in text-guided AI art generation. We introduce a new mathematical foundation for diffusion models…
Diffusion models have recently emerged as a powerful framework for generative modeling. They consist of a forward process that perturbs input data with Gaussian white noise and a reverse process that learns a score function to generate…
Progressively applying Gaussian noise transforms complex data distributions to approximately Gaussian. Reversing this dynamic defines a generative model. When the forward noising process is given by a Stochastic Differential Equation (SDE),…