Related papers: Deterministic Decomposition of Stochastic Generati…

Human trajectory data is crucial in urban planning, traffic engineering, and public health. However, directly using real-world trajectory data often faces challenges such as privacy concerns, data acquisition costs, and data quality. A…

Diffusion-based generative models use stochastic differential equations (SDEs) and their equivalent ordinary differential equations (ODEs) to establish a smooth connection between a complex data distribution and a tractable prior…

We present a field theory for the statistics of charge and current fluctuations in diffusive systems. The cumulant generating function is given by the saddle-point solution for the action of this field theory. The action depends on two…

Recent years have witnessed significant progress in developing effective training and fast sampling techniques for diffusion models. A remarkable advancement is the use of stochastic differential equations (SDEs) and their…

Probabilistic generative models based on measure transport, such as diffusion and flow-based models, are often formulated in the language of Markovian stochastic dynamics, where the choice of the underlying process impacts both algorithmic…

Given a set of $K$ probability densities, we consider the multimarginal generative modeling problem of learning a joint distribution that recovers these densities as marginals. The structure of this joint distribution should identify…

Mathematical models for complex systems are often accompanied with uncertainties. The goal of this paper is to extract a stochastic differential equation governing model with observation on stationary probability distributions. We develop a…

We consider a trait-structured population subject to mutation, birth and competition of logistic type, where the number of coexisting types may fluctuate. Applying a limit of rare mutations to this population while keeping the population…

Learning dynamical systems from incomplete or noisy data is inherently ill-posed, as a single observation may correspond to multiple plausible futures. While physics-based ensemble forecasting relies on perturbing initial states to capture…

We provide a general framework for learning diffusion bridges that transport prior to target distributions. It includes existing diffusion models for generative modeling, but also underdamped versions with degenerate diffusion matrices,…

We propose a deterministic denoising algorithm for discrete-state diffusion models. The key idea is to derandomize the generative reverse Markov chain by introducing a variant of the herding algorithm, which induces deterministic state…

Generative diffusion models have achieved spectacular performance in many areas of machine learning and generative modeling. While the fundamental ideas behind these models come from non-equilibrium physics, variational inference and…

A method is developed to estimate the properties of a global hydrodynamic instability in turbulent flows from measurement data of the limit-cycle oscillations. For this purpose, the flow dynamics are separated in deterministic contributions…

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…

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…

Compared to the existing function-based models in deep generative modeling, the recently proposed diffusion models have achieved outstanding performance with a stochastic-process-based approach. But a long sampling time is required for this…

We propose a new framework for generative modeling based on a discrete-time stochastic control formulation of measure transport. Adapting classic results from control theory, we formulate our problem as a linear program whose dual variables…

A generative model based on a continuous-time normalizing flow between any pair of base and target probability densities is proposed. The velocity field of this flow is inferred from the probability current of a time-dependent density that…

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…

Reconstructing dynamics using samples from sparsely time-resolved snapshots is an important problem in both natural sciences and machine learning. Here, we introduce a new deep learning approach for solving regularized unbalanced optimal…