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Variational autoencoders have been widely applied for natural language generation, however, there are two long-standing problems: information under-representation and posterior collapse. The former arises from the fact that only the last…
We study a generalization of the classical discrete-time, Linear-Quadratic-Gaussian (LQG) control problem where the noise distributions affecting the states and observations are unknown and chosen adversarially from divergence-based…
Turbulent flows posses broadband, power-law spectra in which multiscale interactions couple high-wavenumber fluctuations to large-scale dynamics. Although diffusion-based generative models offer a principled probabilistic forecasting…
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…
We construct and analyze generative diffusions that transport a point mass to a prescribed target distribution over a finite time horizon using the stochastic interpolant framework. The drift is expressed as a conditional expectation that…
Generative diffusion processes are an emerging and effective tool for image and speech generation. In the existing methods, the underline noise distribution of the diffusion process is Gaussian noise. However, fitting distributions with…
Langevin Dynamics has been extensively employed in global non-convex optimization due to the concentration of its stationary distribution around the global minimum of the potential function at low temperatures. In this paper, we propose to…
Discriminator Guidance has become a popular method for efficiently refining pre-trained Score-Matching Diffusion models. However, in this paper, we demonstrate that the standard implementation of this technique does not necessarily lead to…
In this work, we consider the numerical solution of an initial boundary value problem for the distributed order time fractional diffusion equation. The model arises in the mathematical modeling of ultra-slow diffusion processes observed in…
Diffusion models that are based on iterative denoising have been recently proposed and leveraged in various generation tasks like image generation. Whereas, as a way inherently built for continuous data, existing diffusion models still have…
We present a backward diffusion flow (i.e. a backward-in-time stochastic differential equation) whose marginal distribution at any (earlier) time is equal to the smoothing distribution when the terminal state (at a latter time) is…
Discrete flow models (DFMs) have been proposed to learn the data distribution on finite state space, offering a flexible framework as an alternative to discrete diffusion models. A line of recent work has studied samplers for discrete…
Recently, a series of papers proposed deep learning-based approaches to sample from target distributions using controlled diffusion processes, being trained only on the unnormalized target densities without access to samples. Building on…
Gaussian processes are distributions over functions that are versatile and mathematically convenient priors in Bayesian modelling. However, their use is often impeded for data with large numbers of observations, $N$, due to the cubic (in…
We introduce the Glauber Generative Model (GGM), a new class of discrete diffusion models, to obtain new samples from a distribution given samples from a discrete space. GGM deploys a discrete Markov chain called the heat bath dynamics (or…
Recent advances in 3D Gaussian diffusion models suffer from time-intensive denoising and post-denoising processing due to the massive number of Gaussian primitives, resulting in slow generation and limited scalability along sampling…
In this work, we present numerical analysis for a distributed optimal control problem, with box constraint on the control, governed by a subdiffusion equation which involves a fractional derivative of order $\alpha\in(0,1)$ in time. The…
Diffusion-based generative models (DBGMs) perturb data to a target noise distribution and reverse this process to generate samples. The choice of noising process, or inference diffusion process, affects both likelihoods and sample quality.…
We propose a new reinforcement learning (RL) formulation for training continuous-time score-based diffusion models for generative AI to generate samples that maximize reward functions while keeping the generated distributions close to the…
Diffusion models over discrete spaces have recently shown striking empirical success, yet their theoretical foundations remain incomplete. In this paper, we study the sampling efficiency of score-based discrete diffusion models under a…