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Generative modeling within constrained sets is essential for scientific and engineering applications involving physical, geometric, or safety requirements (e.g., molecular generation, robotics). We present a unified framework for…
Diffusion models have gained prominence as state-of-the-art techniques for synthesizing images and videos, particularly due to their ability to scale effectively with large datasets. Recent studies have uncovered that these extensive…
Diffusion-based samplers learn to sample complex, high-dimensional distributions using energies or log densities alone, without training data. Yet, they remain impractical for molecular sampling because they are often slower than molecular…
Learning to sample from complex unnormalized distributions is a fundamental challenge in computational physics and machine learning. While score-based and variational methods have achieved success in continuous domains, extending them to…
Existing approaches to diffusion-based inverse problem solvers frame the signal recovery task as a probabilistic sampling episode, where the solution is drawn from the desired posterior distribution. This framework suffers from several…
Sequential Monte Carlo (SMC), or particle filtering, is a popular class of methods for sampling from an intractable target distribution using a sequence of simpler intermediate distributions. Like other importance sampling-based methods,…
In this paper, we develop and analyze a stochastic algorithm for solving space-time fractional diffusion models, which are widely used to describe anomalous diffusion dynamics. These models pose substantial numerical challenges due to the…
We introduce Diffusion Active Learning, a novel approach that combines generative diffusion modeling with data-driven sequential experimental design to adaptively acquire data for inverse problems. Although broadly applicable, we focus on…
Stochastic differential equation (SDE)-based generative models have achieved substantial progress in conditional generation via training-free differentiable loss-guided approaches. However, existing methodologies utilizing posterior sam-…
Controllable layout generation aims at synthesizing plausible arrangement of element bounding boxes with optional constraints, such as type or position of a specific element. In this work, we try to solve a broad range of layout generation…
Continuous Conditional Diffusion Model (CCDM) is a diffusion-based framework designed to generate high-quality images conditioned on continuous regression labels. Although CCDM has demonstrated clear advantages over prior approaches across…
Diffusion language models (DLMs) are an attractive alternative to autoregressive models because they promise sublinear-time, parallel generation, yet practical gains remain elusive as high-quality samples still demand hundreds of refinement…
Diffusion models have emerged as a powerful class of generative models for molecular design, capable of capturing complex structural distributions and achieving high fidelity in 3D molecule generation. However, their widespread use remains…
Diffusion models have demonstrated remarkable capabilities in visual content generation but remain challenging to deploy due to their high computational cost during inference. This computational burden primarily arises from the quadratic…
We propose a novel class of Sequential Monte Carlo (SMC) algorithms, appropriate for inference in probabilistic graphical models. This class of algorithms adopts a divide-and-conquer approach based upon an auxiliary tree-structured…
Learning models with categorical variables requires optimizing expectations over discrete distributions, a setting in which stochastic gradient-based optimization is challenging due to the non-differentiability of categorical sampling. A…
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…
Despite diffusion models' superior capabilities in modeling complex distributions, there are still non-trivial distributional discrepancies between generated and ground-truth images, which has resulted in several notable problems in image…
Diffusion (score-based) generative models have been widely used for modeling various types of complex data, including images, audios, and point clouds. Recently, the deep connection between forward-backward stochastic differential equations…
We provide a mathematical study of the modified Diffusion Monte Carlo (DMC) algorithm introduced in the companion article \cite{DMC}. DMC is a simulation technique that uses branching particle systems to represent expectations associated…