It is argued that the inductive bias of locality means that the machinery of effective field theory from physics can be usefully applied to describe the denoising dynamics of Brownian motion.
Abstract
We study score-matching diffusion models with a convolutional architecture. We argue that the inductive bias of locality means that the machinery of effective field theory from physics can be usefully applied to describe the denoising dynamics. We apply this formalism first to a simple toy example which permits an analytical description, and thereafter to MNIST, and show that in both cases, the mutual information between two points grows in a manner predicted by a simple effective field theory of Brownian motion.
We construct the natural generalization of stochastic quantization (in the Markovian sense) by considering jump-diffusion processes. This class of stochastic processes exhibits non-continuous paths, so-called L\'evy flights. In the presence of jumps, action landscapes with barriers can be efficiently explored, improving and even restoring ergodicity where traditional diffusion approaches become inefficient. We explore different strategies for constructing efficient jump updates, which we deploy to address the benchmark problem of topological freezing in 2d U(1) gauge theory.
To understand the phenomena displayed in active phase separation, general top-down theories like Active Model B+ (AMB+) add fluxes that break time reversal symmetry. Starting from an Enskog-like kinetic theory of hard-core active Brownian particles in the high persistence regime, we derive AMB+ from first principles. For the effective free energy to have two minima, we propose an effective parametrization of the pair correlation function. Explicit expressions for all coefficients in the model are given as a function of the microscopic parameters to leading order in the P\'eclet number.
We study a class of discrete-time interacting particle systems arising from mean-field coupled maps. We establish a Dobrushin-type estimate, a relative entropy estimate and Central Limit Theorem (CLT) type results for this class of systems. First we control the growth of the 1-Wasserstein distance between the empirical measures and the limiting distributions. Then we use the relative entropy method to show the propagation of chaos. Finally we consider the asymptotic behavior of the fluctuations for the empirical measures and prove that the sequence of fluctuation processes converges in distribution to some Gaussian process, where we establish both qualitative and quantitative results.
We study angular variation in the frontier of branching Brownian motion (BBM) in multiple dimensions. The time average of this frontier is tied to the long-time limit of the critical derivative martingale, which is a random integrable function on the sphere. We show that this function is nowhere locally bounded. As a consequence, BBM exhibits strong persistent anisotropy: there are dense arbitrarily large gaps between the BBM frontier in different directions.
The performance of generative diffusion models is determined by the choice of the reference diffusion process connecting the empirical and prior distributions. Conventional approaches typically trade off simulation-free training against finite-time generation. We propose a framework for designing the reference process that achieves both simultaneously. The key idea is to prescribe tractable time-dependent conditional distributions and then construct the reference process realizing them as its marginals. This framework reveals that score matching is not fundamental to diffusion-model training but instead emerges naturally through reversal of the reference process. We further show that conditional flow matching arises as the small-noise limit of the proposed framework.
A new machine-learning framework aims to improve the success rate of computational protein design while moving away from results that reproduce sequences found in nature.
MIT News · Artificial Intelligence· news.mit.eduAug 24, 2026
