Related papers: Learning Discrete Diffusion of Graphs via Free-Ene…

The use of guidance to steer sampling toward desired outcomes has been widely explored within diffusion models, especially in applications such as image and trajectory generation. However, incorporating guidance during training remains…

Uncertainty propagation and filtering can be interpreted as gradient flows with respect to suitable metrics in the infinite dimensional manifold of probability density functions. Such a viewpoint has been put forth in recent literature, and…

Discrete diffusion has recently emerged as a promising paradigm in discrete data modeling. However, existing methods typically rely on a fixed rate transition matrix during training, which not only limits the expressiveness of latent…

In this paper, we introduce a novel approach for autonomous driving trajectory generation by harnessing the complementary strengths of diffusion probabilistic models (a.k.a., diffusion models) and transformers. Our proposed framework,…

Reinforcement learning fine-tuning has proven effective for steering generative diffusion models toward desired properties in image and molecular domains. Graph diffusion models have similarly been applied to combinatorial structure…

We present a method to downscale idealized geophysical fluid simulations using generative models based on diffusion maps. By analyzing the Fourier spectra of images drawn from different data distributions, we show how one can chain together…

Inspired by the gradient flow viewpoint of the Landau equation and the corresponding dynamic formulation of the Landau metric in [arXiv:2007.08591], we develop a novel implicit particle method for the Landau equation in the framework of the…

Diffusion Models (DMs) have impressive capabilities among generation models, but are limited to slower inference speeds and higher computational costs. Previous works utilize one-shot structure pruning to derive lightweight DMs from…

We develop a novel physics informed deep learning approach for solving nonlinear drift-diffusion equations on metric graphs. These models represent an important model class with a large number of applications in areas ranging from transport…

Diffusion models excel at capturing the natural design spaces of images, molecules, DNA, RNA, and protein sequences. However, rather than merely generating designs that are natural, we often aim to optimize downstream reward functions while…

In this paper we bring together some of the key ideas and methods of two disparate fields of mathematical research, frame theory and optimal transport, using the methods of the second to answer questions posed in the first. In particular,…

In this paper we provide a variational characterisation for a class of non-linear evolution equations with constant non-negative Dirichlet boundary conditions on a bounded domain as gradient flows in the space of non-negative measures. The…

A diffused-interface approach based on the Allen-Cahn phase field equation is developed within a high-order Discontinuous Galerkin framework. The interface capturing technique is based on the balance between explicit diffusion and…

In this paper we present a novel algorithm for simulating geometrical flows, and in particular the Willmore flow, with conservation of volume and area. The idea is to adapt the class of diffusion-redistanciation algorithms to the Willmore…

In this work, we investigate links between the formulation of the flow of marginals of reversible diffusion processes as gradient flows in the space of probability measures and path wise large deviation principles for sequences of such…

In the first part of this paper, we consider a family of continuous-time dynamical systems coupled with diffusion-transmutation processes. Under certain conditions, such randomly perturbed dynamical systems can be interpreted as an averaged…

We introduce a framework for joint grounded scene graph - image generation, a challenging task involving high-dimensional, multi-modal structured data. To effectively model this complex joint distribution, we adopt a factorized approach:…

Recently Data-Free Knowledge Distillation (DFKD) has garnered attention and can transfer knowledge from a teacher neural network to a student neural network without requiring any access to training data. Although diffusion models are adept…

Accurately reconstructing continuous flow fields from sparse or indirect measurements remains an open challenge, as existing techniques often suffer from oversmoothing artifacts, reliance on heterogeneous architectures, and the…

Graph generation is a critical yet challenging task, as empirical analyses require a deep understanding of complex, non-Euclidean structures. Diffusion models have recently made significant advances in graph generation, but these models are…