Related papers: AdjointDEIS: Efficient Gradients for Diffusion Mod…

In recent years we have witnessed a growth in mathematics for deep learning, which has been used to solve inverse problems of partial differential equations (PDEs). However, most deep learning-based inversion methods either require paired…

The past few years have witnessed the great success of Diffusion models~(DMs) in generating high-fidelity samples in generative modeling tasks. A major limitation of the DM is its notoriously slow sampling procedure which normally requires…

Abstract Diffusion models have recently gained prominence as a novel category of generative models. Despite their success, these models face a notable drawback in terms of slow sampling speeds, requiring a high number of function…

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…

We present a concise, self-contained derivation of diffusion-based generative models. Starting from basic properties of Gaussian distributions (densities, quadratic expectations, re-parameterisation, products, and KL divergences), we…

Stochastic differential equations (SDEs) using jump-diffusion processes describe many natural phenomena at the microscopic level. Since they are commonly used to model economic and financial evolutions, the calibration and optimal control…

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…

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…

We introduce Adjoint Sampling, a highly scalable and efficient algorithm for learning diffusion processes that sample from unnormalized densities, or energy functions. It is the first on-policy approach that allows significantly more…

Diffusion probabilistic models (DPMs) are emerging powerful generative models. Despite their high-quality generation performance, DPMs still suffer from their slow sampling as they generally need hundreds or thousands of sequential function…

Drawing from the theory of stochastic differential equations, we introduce a novel sampling method for known distributions and a new algorithm for diffusion generative models with unknown distributions. Our approach is inspired by the…

Diffusion or flow-based models are powerful generative paradigms that are notoriously hard to sample as samples are defined as solutions to high-dimensional Ordinary or Stochastic Differential Equations (ODEs/SDEs) which require a large…

Diffusion models have emerged as powerful generative tools with applications in computer vision and scientific machine learning (SciML), where they have been used to solve large-scale probabilistic inverse problems. Traditionally, these…

We study the problem of training diffusion and flow generative models to sample from target distributions defined by an exponential tilting of a base density; a formulation that subsumes both sampling from unnormalized densities and reward…

Recently, diffusion models have achieved great success in generative tasks. Sampling from diffusion models is equivalent to solving the reverse diffusion stochastic differential equations (SDEs) or the corresponding probability flow…

Diffusion models (DMs) have become the dominant paradigm of generative modeling in a variety of domains by learning stochastic processes from noise to data. Recently, diffusion denoising bridge models (DDBMs), a new formulation of…

Diffusion models (DMs) have revolutionized generative learning. They utilize a diffusion process to encode data into a simple Gaussian distribution. However, encoding a complex, potentially multimodal data distribution into a single…

Score-based generative models, which transform noise into data by learning to reverse a diffusion process, have become a cornerstone of modern generative AI. This paper contributes to establishing theoretical guarantees for the probability…

In this work, we present an adjoint-based method for discovering the underlying governing partial differential equations (PDEs) given data. The idea is to consider a parameterized PDE in a general form and formulate a PDE-constrained…

Diffusion-based inverse algorithms have shown remarkable performance across various inverse problems, yet their reliance on numerous denoising steps incurs high computational costs. While recent developments of fast diffusion ODE solvers…