Related papers: Non-asymptotic convergence bound of conditional di…

Classical methods in robot motion planning, such as sampling-based and optimization-based methods, often struggle with scalability towards higher-dimensional state spaces and complex environments. Diffusion models, known for their…

This article studies the achievable guarantees on the error rates of certain learning algorithms, with particular focus on refining logarithmic factors. Many of the results are based on a general technique for obtaining bounds on the error…

Deep neural networks are known to be overconfident when applied to out-of-distribution (OOD) inputs which clearly do not belong to any class. This is a problem in safety-critical applications since a reliable assessment of the uncertainty…

We develop a quantitative statistical theory of transformers in the large-context regime by adopting the abstraction of contextual flow maps (CFMs): dynamical systems that evolve a distinguished token in the presence of a contextual measure…

Inference-time guided sampling steers state-of-the-art diffusion and flow models without fine-tuning by interpreting the generation process as a controllable trajectory. This provides a simple and flexible way to inject external constraints…

Diffusion models have shown great promise in synthesizing visually appealing images. However, it remains challenging to condition the synthesis at a fine-grained level, for instance, synthesizing image pixels following some generic color…

This work considers the inverse dynamic source problem arising from the time-domain fluorescence diffuse optical tomography (FDOT). We recover the dynamic distributions of fluorophores in biological tissue by the one single boundary…

On a smooth bounded Euclidean domain, Sobolev-subcritical fast diffusion with vanishing boundary trace is known to lead to finite-time extinction, with a vanishing profile selected by the initial datum. In rescaled variables, we quantify…

Supervised machine learning has enabled accurate pathology detection in brain MRI, but requires training data from diseased subjects that may not be readily available in some scenarios, for example, in the case of rare diseases.…

This paper investigates the near optimal control for a kind of linear stochastic control systems governed by the forward backward stochastic differential equations, where both the drift and diffusion terms are allowed to depend on controls…

This work presents an extensive hyperparameter search on Image Diffusion Models for Echocardiogram generation. The objective is to establish foundational benchmarks and provide guidelines within the realm of ultrasound image and video…

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…

This paper focuses on Bayesian inference in a federated learning context (FL). While several distributed MCMC algorithms have been proposed, few consider the specific limitations of FL such as communication bottlenecks and statistical…

Generative models such as diffusion models have achieved remarkable success in state-of-the-art image and text tasks. Recently, score-based diffusion models have extended their success beyond image generation, showing competitive…

Graph Neural Networks (GNNs)-based recommendation algorithms typically assume that training and testing data are drawn from independent and identically distributed (IID) spaces. However, this assumption often fails in the presence of…

We consider a system of semilinear partial differential equations (PDEs) with a nonlinearity depending on both the solution and its gradient. The Neumann boundary condition depends on the solution in a nonlinear manner. The uniform…

We discuss a connection between a generative model, called the diffusion model, and nonequilibrium thermodynamics for the Fokker-Planck equation, called stochastic thermodynamics. Using techniques from stochastic thermodynamics, we derive…

We develop theory to understand an intriguing property of diffusion models for image generation that we term critical windows. Empirically, it has been observed that there are narrow time intervals in sampling during which particular…

Score diffusion methods can learn probability densities from samples. The score of the noise-corrupted density is estimated using a deep neural network, which is then used to iteratively transport a Gaussian white noise density to a target…

This paper focuses on investigating an inexact stochastic model-based optimization algorithm that integrates preconditioning techniques for solving stochastic composite optimization problems. The proposed framework unifies and extends the…