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Bayesian flow networks (BFNs) iteratively refine the parameters, instead of the samples in diffusion models (DMs), of distributions at various noise levels through Bayesian inference. Owing to its differentiable nature, BFNs are promising…

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…

Residual networks are an Euler discretization of solutions to Ordinary Differential Equations (ODE). This paper explores a deeper relationship between Transformer and numerical ODE methods. We first show that a residual block of layers in…

This paper introduces two key contributions aimed at improving the speed and quality of images generated through inverse diffusion processes. The first contribution involves reparameterizing the diffusion process in terms of the angle on a…

Conditioning image generation facilitates seamless editing and the creation of photorealistic images. However, conditioning on noisy or Out-of-Distribution (OoD) images poses significant challenges, particularly in balancing fidelity to the…

This paper presents a fast, principled approach for detecting anomalous and out-of-distribution (OOD) samples in deep neural networks (DNN). We propose the application of linear statistical dimensionality reduction techniques on the…

Time-series data in real-world medical settings typically exhibit long-range dependencies and are observed at non-uniform intervals. In such contexts, traditional sequence-based recurrent models struggle. To overcome this, researchers…

Diffusion probabilistic models (DPMs), while effective in generating high-quality samples, often suffer from high computational costs due to their iterative sampling process. To address this, we propose an enhanced ODE-based sampling method…

Embedding nonlinear dynamical systems into artificial neural networks is a powerful new formalism for machine learning. By parameterizing ordinary differential equations (ODEs) as neural network layers, these Neural ODEs are…

Continuous normalizing flows (CNFs) are an attractive generative modeling technique, but they have been held back by limitations in their simulation-based maximum likelihood training. We introduce the generalized conditional flow matching…

Statistical surrogate modeling of fluid flows is hard because dynamics are multiscale and highly sensitive to initial conditions. Conditional diffusion surrogates can be accurate, but usually need hundreds of stochastic sampling steps. We…

Recently, diffusion models (DMs) have made significant strides in high-quality image generation. However, the multi-step denoising process often results in considerable computational overhead, impeding deployment on resource-constrained…

The curvature of ODE trajectories in diffusion models hinders their ability to generate high-quality images in a few number of function evaluations (NFE). In this paper, we propose a novel and effective approach to reduce trajectory…

We propose a new finetuning method to provide pre-trained large language models (LMs) the ability to scale test-time compute through the diffusion framework. By increasing the number of diffusion steps, we show our finetuned models achieve…

Diffusion models (DMs) are a powerful generative framework that have attracted significant attention in recent years. However, the high computational cost of training DMs limits their practical applications. In this paper, we start with a…

Neural Ordinary Differential Equations (NODEs) use a neural network to model the instantaneous rate of change in the state of a system. However, despite their apparent suitability for dynamics-governed time-series, NODEs present a few…

A normalizing flow (NF) is a mapping that transforms a chosen probability distribution to a normal distribution. Such flows are a common technique used for data generation and density estimation in machine learning and data science. The…

We introduce an ordinary differential equation (ODE) based deep generative method for learning conditional distributions, named Conditional F\"ollmer Flow. Starting from a standard Gaussian distribution, the proposed flow could approximate…

Reinforcement learning (RL) has become an effective way to improve prompt alignment and perceptual quality in diffusion and flow-matching generators. A critical step for applying online RL to flow matching is turning the deterministic…

Numerical simulation of ordinary differential equations (ODEs) can be challenging when the system exhibits high accelerations and rapidly changing dynamics. Under these conditions the ODE solver often needs to take very small time steps in…