Related papers: DPAC: Distribution-Preserving Adversarial Control …
While the mathematical foundations of score-based generative models are increasingly well understood for unconstrained Euclidean spaces, many practical applications involve data restricted to bounded domains. This paper provides a…
Diffusion guidance is a powerful technique that enables controllable and high-fidelity sample generation with diffusion models. At a high level, it modifies the score function by incorporating a guidance term that steers the generative…
The inherent complexity of boundary plasma, characterized by multi-scale and multi-physics challenges, has historically restricted high-fidelity simulations to scientific research due to their intensive computational demands. Consequently,…
We study sparse optimal control of a non-local continuity equation, where the goal is to steer a distribution via finitely many controllable agents or actuators. This model arises naturally in mean-field multi-agent systems and takes the…
We analyze an optimal control problem with pointwise tracking for a fractional semilinear elliptic partial differential equation. The diffusion is characterized by the spectral fractional Laplacian $(-\Delta)^s$ with $s \in (1/2,1)$, a…
Motivated by recent work on approximation of diffusion equations by deterministic interacting particle systems, we develop a nonlocal approximation for a range of linear and nonlinear diffusion equations and prove convergence of the method…
Langevin Dynamics is a Stochastic Differential Equation (SDE) central to sampling and generative modeling and is implemented via time discretization. Langevin Monte Carlo (LMC), based on the Euler-Maruyama discretization, is the simplest…
Generative adversarial networks are a novel method for statistical inference that have achieved much empirical success; however, the factors contributing to this success remain ill-understood. In this work, we attempt to analyze generative…
Diffusion policies excel at visuomotor control but often fail catastrophically under severe out-of-distribution (OOD) disturbances, such as unexpected object displacements or visual corruptions. To address this vulnerability, we introduce…
We introduce and study a class of probabilistic generative models, where the latent object is a finite-dimensional diffusion process on a finite time interval and the observed variable is drawn conditionally on the terminal point of the…
Optimal transport with quadratic cost provides a geometric framework for steering an ensemble, modeled by a probability law, with minimal effort. Yet ambient-space formulations become unwieldy in high dimensions, and sensing or actuation in…
Diffusion models have recently emerged as effective generative frameworks for trajectory optimization, capable of producing high-quality and diverse solutions. However, training these models in a purely data-driven manner without explicit…
Recent advancements in diffusion models have made fine-tuning text-to-image models for personalization increasingly accessible, but have also raised significant concerns regarding unauthorized data usage and privacy infringement. Current…
Classifier-guided diffusion models generate conditional samples by augmenting the reverse-time score with the gradient of the log-probability predicted by a probabilistic classifier. In practice, this classifier is usually obtained by…
Deep learning models are known to be vulnerable to adversarial attacks by injecting sophisticated designed perturbations to input data. Training-time defenses still exhibit a significant performance gap between natural accuracy and robust…
This study investigates the impact of gradient compression on distributed training performance, focusing on sparsification and quantization techniques, including top-k, DGC, and QSGD. In baseline experiments, random-k compression results in…
Sampling-based methods have become a cornerstone of contemporary approaches to Model Predictive Control (MPC), as they make no restrictions on the differentiability of the dynamics or cost function and are straightforward to parallelize.…
Diffusion models, which convert noise into new data instances by learning to reverse a diffusion process, have become a cornerstone in contemporary generative modeling. In this work, we develop non-asymptotic convergence theory for a…
We consider an optimal control problem that entails the minimization of a nondifferentiable cost functional, fractional diffusion as state equation and constraints on the control variable. We provide existence, uniqueness and regularity…
Out-of-distribution (OOD) detection remains a fundamental challenge for deep neural networks, particularly due to overconfident predictions on unseen OOD samples during testing. We reveal a key insight: OOD samples predicted as the same…