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I'll present how we can use diffusion models and closely related energy-based models to solve different reasoning tasks. I'll talk about how these models naturally enable us to implement search at inference time, and how these models can be composed together to solve more complex reasoning questions. Finally, I'll empirically illustrate how such a reasoning system allows us to solve a number of complex symbolic reasoning and decision-making/planning tasks.

In this talk, I'll discuss how diffusion and flow models transformed continuous-action policies in RL and robotic control. While in principle learning-based control methods (imitation learning and RL) are largely agnostic to the particular representation used for the action distribution, in practice diffusion and flow models have significantly improved the performance of learned policies across various learning-based control domains. By modeling complex distributions over high-dimensional spaces, these models made it possible to represent large "action chunks" (sequences of actions), which greatly improved imitation learning performance and, most recently, the performance of offline RL and offline-to-online RL methods. In this talk, I'll discuss algorithms that use diffusion and flow for RL and IL, as well as some of the large-scale models built on these principles.

Diffusion models rely on reversing a forward diffusion process modeled by a stochastic differential equation, a non-equilibrium process at its core. In this talk, I will outline an alternative formulation that relies solely on Langevin MCMC at a fixed noise level. In this framework, the effective noise is reduced through the accumulation of noisy measurements. Furthermore, by choosing an appropriate noise level, one can guarantee that the measurement accumulation remains within the class of log-concave sampling problems. Time permitting, I will discuss new extensions of Langevin MCMC for discrete data that are related to discrete diffusion models.

We consider classifying labelled data in the interpolation regime where there exist linear classifiers (with possibly negative margin) correctly classifying all points in the dataset. Under two idealized data-generating distributions, we establish a large deviation principle on the event that a point chosen uniformly at random from the set of interpolators achieves a given generalization error. This allows us to describe the proportion of interpolators having any desired performance and establish a concentration result regarding the most typical performance. We remark that this typical performance is inferior to that of ERM by gradient descent, indicating that most interpolators are ‘bad’. Sampling such typical interpolators is an interesting open problem.

This is based on joint work with August Chen.

Modern generative AI is often viewed through two dominant paradigms: autoregressive models, which underpin much of language modeling, and diffusion models, which have set the standard for high-quality image and video synthesis. These paradigms are usually treated as fundamentally different: autoregressive models are associated with compression and sequential computation, while diffusion models are associated with perceptual sample quality and parallel generation.

In this talk, I will argue that this divide is less fundamental than it may appear. I will use masked diffusion models (MDMs) as a lens: this class of discrete diffusion models is theoretically equivalent to random-order autoregressive models. From this perspective, many empirical differences between autoregression and diffusion, such as parallelism and perceptual quality, arise not from a fundamental distinction between the model classes themselves, but from details of model specification and training techniques. For example, I will present evidence that the loss reweighting technique from diffusion, when applied to any-order MDM/AR models, can yield perceptual sample quality comparable to strong continuous diffusion models.

Next, I will talk about moving beyond both (fixed-order) autoregression and (random-order) diffusion to find new powerful ways of generation. Specifically, I will focus on models that adaptively determine their generation order based on partial context. I will highlight the important role of insertion in flexible generation and planning, and a principled framework we established for scalable maximum likelihood learning of insertion-based generative models.