Related papers: Score dynamics: scaling molecular dynamics with pi…

This work proposes stochastic partial differential equations (SPDEs) as a practical tool to replicate clustering effects of more detailed particle-based dynamics. Inspired by membrane-mediated receptor dynamics on cell surfaces, we…

Score-based diffusion models are a highly effective method for generating samples from a distribution of images. We consider scenarios where the training data comes from a noisy version of the target distribution, and present an efficiently…

We propose an observation-driven modeling framework that allows model parameters to vary over time through an implicit score-driven (ISD) update. The ISD update maximizes the logarithmic observation density with respect to the parameter…

Distribution shifts between training and testing datasets significantly impair the model performance on graph learning. A commonly-taken causal view in graph invariant learning suggests that stable predictive features of graphs are causally…

Multiscale dynamical systems characterized by interacting fast and slow processes are ubiquitous across scientific domains, from climate dynamics to fluid mechanics. Accurate modeling of such systems requires capturing both the long-term…

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…

Score-based diffusion models represent a significant variant within the diffusion model family and have seen extensive application in the increasingly popular domain of generative tasks. Recent investigations have explored the denoising…

Score distillation sampling~(SDS) has been widely adopted to overcome the absence of unseen views in reconstructing 3D objects from a \textbf{single} image. It leverages pre-trained 2D diffusion models as teacher to guide the reconstruction…

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…

Many real-world optimization problems contain parameters that are unknown before deployment time, either due to stochasticity or to lack of information (e.g., demand or travel times in delivery problems). A common strategy in such cases is…

Multiple time scale molecular dynamics enhances computational efficiency by updating slow motions less frequently than fast motions. However, in practice the largest outer time step possible is limited not by the physical forces but by…

This paper studies the original discrete-time denoising diffusion probabilistic model (DDPM) from a probabilistic point of view. We present three main theoretical results. First, we show that the time-dependent score function associated…

Causal discovery from observational data is a fundamental task in artificial intelligence, with far-reaching implications for decision-making, predictions, and interventions. Despite significant advances, existing methods can be broadly…

Score-based diffusion models have emerged as a powerful class of generative methods, achieving state-of-the-art performance across diverse domains. Despite their empirical success, the mathematical foundations of those models remain only…

In recent years, diffusion models trained on equilibrium molecular distributions have proven effective for sampling biomolecules. Beyond direct sampling, the score of such a model can also be used to derive the forces that act on molecular…

Multi-target detection (MTD) is the problem of estimating an image from a large, noisy measurement that contains randomly translated and rotated copies of the image. Motivated by the single-particle cryo-electron microscopy technology, we…

We introduce a novel class of score-based diffusion processes that operate directly in the representation space of Lie groups. Leveraging the framework of Generalized Score Matching, we derive a class of Langevin dynamics that decomposes as…

We analyse how the sampling dynamics of distributions evolve in score-based diffusion models using cross-fluctuations, a centered-moment statistic from statistical physics. Specifically, we show that starting from an unbiased isotropic…

Translational diffusion coefficients are routinely estimated from molecular dynamics simulations. Linear fits to mean squared displacement (MSD) curves have become the de facto standard, from simple liquids to complex biomacromolecules.…

Conditional diffusion models provide a natural framework for probabilistic prediction of dynamical systems and have been successfully applied to fluid dynamics and weather prediction. However, in many settings, the available information at…