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Diffusion models have exhibited excellent performance in various domains. The probability flow ordinary differential equation (ODE) of diffusion models (i.e., diffusion ODEs) is a particular case of continuous normalizing flows (CNFs),…

Diffusion-based generative models employ stochastic differential equations (SDEs) and their equivalent probability flow ordinary differential equations (ODEs) to establish a smooth transformation between complex high-dimensional data…

Inverse problems describe the process of estimating the causal factors from a set of measurements or data. Mapping of often incomplete or degraded data to parameters is ill-posed, thus data-driven iterative solutions are required, for…

Reinforcement Learning from Human Feedback (RLHF) is increasingly used to fine-tune diffusion models, but a key challenge arises from the mismatch between stochastic samplers used during training and deterministic samplers used during…

We introduce a novel paradigm for learning non-parametric drift and diffusion functions for stochastic differential equation (SDE). The proposed model learns to simulate path distributions that match observations with non-uniform time…

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,…

How do diffusion generative models convert pure noise into meaningful images? In a variety of pretrained diffusion models (including conditional latent space models like Stable Diffusion), we observe that the reverse diffusion process that…

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 propose an inference-time scaling approach for pretrained flow models. Recently, inference-time scaling has gained significant attention in LLMs and diffusion models, improving sample quality or better aligning outputs with user…

Various bias-correction methods such as EXTRA, gradient tracking methods, and exact diffusion have been proposed recently to solve distributed {\em deterministic} optimization problems. These methods employ constant step-sizes and converge…

Diffusion models generate high-quality synthetic data. They operate by defining a continuous-time forward process which gradually adds Gaussian noise to data until fully corrupted. The corresponding reverse process progressively "denoises"…

Score-based generative models have excellent performance in terms of generation quality and likelihood. They model the data distribution by matching a parameterized score network with first-order data score functions. The score network can…

Sampling in score-based diffusion models can be performed by solving either a reverse-time stochastic differential equation (SDE) parameterized by an arbitrary time-dependent stochasticity parameter or a probability flow ODE, corresponding…

Higher-order ODE solvers have become a standard tool for accelerating diffusion probabilistic model (DPM) sampling, motivating the widespread view that first-order methods are inherently slower and that increasing discretization order is…

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,…

We propose DiffSep, a new single channel source separation method based on score-matching of a stochastic differential equation (SDE). We craft a tailored continuous time diffusion-mixing process starting from the separated sources and…

Diffusion-based generative models have achieved remarkable performance across various domains, yet their practical deployment is often limited by high sampling costs. While prior work focuses on training objectives or individual solvers,…

Diffusion Models (DMs) have achieved great success in image generation and other fields. By fine sampling through the trajectory defined by the SDE/ODE solver based on a well-trained score model, DMs can generate remarkable high-quality…

Straightening the probability flow of the continuous-time generative models, such as diffusion models or flow-based models, is the key to fast sampling through the numerical solvers, existing methods learn a linear path by directly…

Reconstructing PDE solutions from sparse observations is a core challenge in scientific computing. We present FM4PDE, a flow-matching generative framework that learns the joint distribution of PDE coefficients (or initial states) and…