Related papers: Port--Hamiltonian Diffusion Models: A Control-Theo…
Diffusion guidance is a powerful technique that enables controllable and high-fidelity sample generation with diffusion models. At a high level, it modifies the score function by incorporating a guidance term that steers the generative…
Denoising diffusion models are a class of generative models which have recently achieved state-of-the-art results across many domains. Gradual noise is added to the data using a diffusion process, which transforms the data distribution into…
Diffusion models achieve state-of-the-art performance in various generation tasks. However, their theoretical foundations fall far behind. This paper studies score approximation, estimation, and distribution recovery of diffusion models,…
Diffusion models are a class of generative models that learn to synthesize samples by inverting a diffusion process that gradually maps data into noise. While these models have enjoyed great success recently, a full theoretical…
Score-based generative models (SGMs) are powerful tools to sample from complex data distributions. Their underlying idea is to (i) run a forward process for time $T_1$ by adding noise to the data, (ii) estimate its score function, and (iii)…
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…
Score-based diffusion models have significantly advanced generative deep learning for image processing. Measurement conditioned models have also been applied to inverse problems such as CT reconstruction. However, the conventional approach,…
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…
We propose closed-form conditional diffusion models for data assimilation. Diffusion models use data to learn the score function (defined as the gradient of the log-probability density of a data distribution), allowing them to generate new…
Score-based modeling through stochastic differential equations (SDEs) has provided a new perspective on diffusion models, and demonstrated superior performance on continuous data. However, the gradient of the log-likelihood function, i.e.,…
Conventional diffusion models typically relies on a fixed forward process, which implicitly defines complex marginal distributions over latent variables. This can often complicate the reverse process' task in learning generative…
By formulating data samples' formation as a Markov denoising process, diffusion models achieve state-of-the-art performances in a collection of tasks. Recently, many variants of diffusion models have been proposed to enable controlled…
Diffusion models have led to significant advancements in generative modelling. Yet their widespread adoption poses challenges regarding data attribution and interpretability. In this paper, we aim to help address such challenges in…
Diffusion Probabilistic Models (DPMs) have recently demonstrated impressive results on various generative tasks.Despite its promises, the learned representations of pre-trained DPMs, however, have not been fully understood. In this paper,…
This paper proposes to build a bridge between microscopic descriptions of matter with internal energy, composed of many fast interacting particles inside an environment, and their port-Hamiltonian (PH) descriptions at macroscopic scale. The…
This paper develops a rigorous probabilistic framework that extends denoising diffusion models to the setting of noncommutative random variables. Building on Voiculescu's theory of free entropy and free Fisher information, we formulate…
Score-based stochastic denoising models have recently been demonstrated as powerful machine learning tools for conditional and unconditional image generation. The existing methods are based on a forward stochastic process wherein the…
Diffusion models have emerged as effective distribution estimators in vision, language, and reinforcement learning, but their use as priors in downstream tasks poses an intractable posterior inference problem. This paper studies amortized…
We present a novel and flexible data-driven framework for estimating the response of higher-order moments of nonlinear stochastic systems to small external perturbations. The classical Generalized Fluctuation--Dissipation Theorem (GFDT)…
We present a mechanism to steer the sampling diversity of denoising diffusion and flow matching models, allowing users to sample from a sharper or broader distribution than the training distribution. We build on the observation that these…