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The blooming diffusion probabilistic models (DPMs) have garnered significant interest due to their impressive performance and the elegant inspiration they draw from physics. While earlier DPMs relied upon the Markovian assumption, recent…

Flow matching has emerged as a simulation-free alternative to diffusion-based generative modeling, producing samples by solving an ODE whose time-dependent velocity field is learned along an interpolation between a simple source…

Normalizing flows are a powerful technique for obtaining reparameterizable samples from complex multimodal distributions. Unfortunately, current approaches are only available for the most basic geometries and fall short when the underlying…

We introduce a new paradigm for generative modeling built on Continuous Normalizing Flows (CNFs), allowing us to train CNFs at unprecedented scale. Specifically, we present the notion of Flow Matching (FM), a simulation-free approach for…

Normalizing Flows are generative models that directly maximize the likelihood. Previously, the design of normalizing flows was largely constrained by the need for analytical invertibility. We overcome this constraint by a training procedure…

We propose a novel machine learning method for sampling from the high-dimensional probability distributions of Lattice Field Theories, which is based on a single neural ODE layer and incorporates the full symmetries of the problem. We test…

Diffusion models have shown great promise for image and video generation, but sampling from state-of-the-art models requires expensive numerical integration of a generative ODE. One approach for tackling this problem is rectified flows,…

We introduce multigrid Predictive Filter Flow (mgPFF), a framework for unsupervised learning on videos. The mgPFF takes as input a pair of frames and outputs per-pixel filters to warp one frame to the other. Compared to optical flow used…

We propose a novel learning framework using neural mean-field (NMF) dynamics for inference and estimation problems on heterogeneous diffusion networks. Our new framework leverages the Mori-Zwanzig formalism to obtain an exact evolution…

We propose Riemannian Denoising Diffusion Probabilistic Models (RDDPMs) for learning distributions on submanifolds of Euclidean space that are level sets of functions, including most of the manifolds relevant to applications. Existing…

Generative models based on dynamical equations such as flows and diffusions offer exceptional sample quality, but require computationally expensive numerical integration during inference. The advent of consistency models has enabled…

Sampling from high-dimensional, multi-modal distributions remains a fundamental challenge across domains such as statistical Bayesian inference and physics-based machine learning. In this paper, we propose Annealing Flow (AF), a method…

We are interested in derivative-free optimization of high-dimensional functions. The sample complexity of existing methods is high and depends on problem dimensionality, unlike the dimensionality-independent rates of first-order methods.…

Inthischapterwediscusshowtolearnanoptimalmanifoldpresentationto regularize nonegative matrix factorization (NMF) for data representation problems. NMF,whichtriestorepresentanonnegativedatamatrixasaproductoftwolowrank nonnegative matrices,…

Modern reinforcement learning (RL) algorithms have found success by using powerful probabilistic models, such as transformers, energy-based models, and diffusion/flow-based models. To this end, RL researchers often choose to pay the price…

Normalizing Flows (NFs) are universal density estimators based on Neural Networks. However, this universality is limited: the density's support needs to be diffeomorphic to a Euclidean space. In this paper, we propose a novel method to…

While the manifold hypothesis is widely adopted in modern machine learning, complex data is often better modeled as stratified spaces -- unions of manifolds (strata) of varying dimensions. Stratified learning is challenging due to varying…

We introduce Random Projection Flows (RPFs), a principled framework for injective normalizing flows that leverages tools from random matrix theory and the geometry of random projections. RPFs employ random semi-orthogonal matrices, drawn…

One-step generative modeling has emerged as a leading approach to amortize the inference cost of diffusion and flow-matching models. Among distillation-free methods, MeanFlow training is notoriously unstable, with non-decreasing loss and…

Symmetry is fundamental to understanding physical systems and can improve performance and sample efficiency in machine learning. Both pursuits require knowledge of the underlying symmetries in data, yet discovering these symmetries…