Spring 2026




If time permits, I will also briefly introduce self-consistent stochastic interpolants, which enable generative modeling from indirect, noisy observations and substantially extend applicability to many scientific and engineering problems where clean data are unavailable.





Based on joint work with Vishesh Jain, Na Lin, Yuanyuan Liu, Natesh Pillai, Ashwin Sah, Mehtaab Sawhney, and Vinod Vaikuntanathan.




In this talk, we first establish a remarkable connection between the zigzag sampler and a variant of Hamiltonian Monte Carlo based on Laplace-distributed momentum. The position-velocity component of the corresponding Hamiltonian dynamics travels along a zigzag path paralleling the Markovian zigzag process; however, the dynamics is non-Markovian as the momentum component encodes non-immediate pasts. In the limit of increasingly frequent momentum refreshments in which we preserve its direction but re-sample magnitude, we prove that Hamiltonian zigzag converges strongly to its Markovian counterpart. This theoretical insight in particular explains the two zigzags' relative performance on target distributions with highly correlated parameters, which we demonstrate on a 11,235-dimensional truncated Gaussian target arising from Bayesian phylogenetic multivariate probit model applied to an HIV virus dataset. We then proceed to construct a Hamiltonian counterpart to the bouncy particle sampler (BPS), further strengthening the connection between the two paradigms. We achieve this by turning BPS's Poisson schedule for velocity switch events into a deterministic one dictated by an auxiliary "inertia" parameter. The resulting Hamiltonian BPS constitutes an efficient sampler on log-concave targets and straightforwardly accommodates parameter constraints. We demonstrate its competitive performance in the posterior computation under Bayesian sparse logistic regression model applied to a large-scale observational study consisting of 72,489 patients and 22,175 clinical covariates. 





To address these challenges, we introduce a principled Sequential Monte Carlo (SMC) framework that formalizes diffusion-based samplers as proposal mechanisms while systematically correcting their biases. The key idea is to construct informative intermediate target distributions that progressively guide particles toward the final distribution of interest. Although the ideal targets are intractable, we derive exact approximations using quantities already available from the score-based proposal, requiring no extra inference overhead. The resulting method, Reverse Diffusion Sequential Monte Carlo, enables consistent sampling and unbiased estimation of the target normalization constant. We demonstrate our method on a range of synthetic targets and Bayesian regression tasks. 










Generalizing results from existing literature, we establish provable guarantees for the Sequential Monte Carlo algorithm and related particle filtering approaches, which have recently found success empirically in the context of both language modeling and diffusion. In particular, our theory identifies a few properties of the oracle which suffice for efficient sampling. We conduct experiments to show that these properties indeed correlate with sampling performance for certain language modeling tasks. 

The efficacy of such sampling algorithms, however, is limited by the relationship between the underlying LLM and the particular sampling task at hand, which has motivated the framework of Test-Time Training (TTT). In particular, TTT updates a model's weights in response to partial generations and reward feedback received at inference time. In the latter half of the talk, we will discuss some provable benefits of TTT in the context of our sampling framework. 

Based on https://arxiv.org/pdf/2603.07887 (joint work with Fan Chen, Dhruv Rohatgi, Raghav Singhal, Carles Domingo-Enrich, Dylan J. Foster, and Akshay Krishnamurthy); and upcoming joint work with Ankur Moitra and Dhruv Rohatgi.