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We view drifting from a Wasserstein gradient flow (WGF) perspective and propose a conservative method for one-step generative modeling, replacing the original displacement-based velocity with a KDE-gradient field given by the difference between kernel-smoothed data and model scores. Using a joint-entropy identity, we establish continuous-time finite-particle bounds on R^d, including a root residual-velocity rate of N^{-1/(d+4)} under bandwidth-uniform quadrature regularity. We also analyze the original non-conservative Laplace-kernel method through a sharp companion-kernel decomposition and show how the resulting residual-velocity bounds yield explicit one-step generation guarantees in terms of the drift size.

Diffusion models generate high-quality synthetic data. They operate by defining a continuous-time forward process which gradually adds Gaussian noise to data until fully corrupted. The corresponding reverse process progressively "denoises" a Gaussian sample into a sample from the data distribution. However, generating high-quality outputs requires many discretization steps to obtain a faithful approximation of the reverse process. This is expensive and has motivated the development of many acceleration methods. We propose to accomplish sample generation by learning the posterior {\em distribution} of clean data samples given their noisy versions, instead of only the mean of this distribution. This allows us to sample from the probability transitions of the reverse process on a coarse time scale, significantly accelerating inference with minimal degradation of the quality of the output. This is accomplished by replacing the standard regression loss used to estimate conditional means with a scoring rule. We validate our method on image and robot trajectory generation, where we consistently outperform standard diffusion models at few discretization steps.

Reinforcement learning has become a central tool for post-training generative models, especially large language models. Recently, there has been growing interest in applying RL to diffusion models. However, directly applying LLM-style RL along the denoising trajectory is inefficient and memory-intensive. In this talk, I will discuss a systematic study of the RL design space for diffusion models, including policy optimization objectives, likelihood estimation, and rollout schemes. Our key finding is that replacing trajectory-based likelihood estimation with an ELBO-based estimator induced by the linear forward process is crucial for efficiency. This also decouples rollout from training, enabling fast ODE samplers. Based on these insights, we develop RL algorithms for diffusion fine-tuning that are an order of magnitude faster than trajectory-based methods. Time permitting, I will also discuss a related stochastic-control approach based on first-order optimization.

We present an algorithmic framework for high-accuracy sampling using unbiased stochastic queries, with two main applications:
Algorithms for diffusion model sampling which obtain $\delta$-error in $\mathrm{polylog}(1/\delta)$ steps, given access to $\widetilde O(\delta)$-accurate score estimates in $L^2$. This is an exponential improvement over all previous results. (ICML 2026, https://arxiv.org/abs/2602.01338)
High-accuracy guarantees for log-concave sampling -- that is, iteration and query complexities which scale as $\mathrm{polylog}(1/\delta)$, where $\delta$ is the desired target accuracy -- are achievable using stochastic gradients with subexponential tails. Notably, this exhibits a separation with the problem of convex optimization, where stochasticity (even additive Gaussian noise) in the gradient oracle incurs $\mathrm{poly}(1/\delta)$ queries. (CoLT 2026, https://arxiv.org/abs/2602.14342)

A sequence of sparse weighted graphs G_N indexed by the number of vertices
N is said to be left-convergent if all (suitably weighted) subgraph counts
converge to a limit as N diverges. This notion generalizes in a
natural way Benjamini-Schramm's definition of local-weak convergence.
A broad research agenda aims at determining which `global' graph properties
determined by left or local-weak convergence (in other words, which
of these properties are in fact local).

We prove that, under a spectral condition on the weighted adjacency matrices
A_N of graph G_N, the free energy density of the Ising model on
this weighted graph is continuous in the left convergence topology
(hence is a local function.)

We use stochastic dynamics as a proof device.
[Based on joint work with Michael Ren]