Spring 2026
Tuesday, January 13, 2026
Title: Stability, instability, and extension of variational inference
Abstract: Variational inference (VI) is a popular alternative to Markov chain Monte Carlo (MCMC) for approximating high-dimensional target distributions. At its core, VI approximates a high-dimensional target distribution—typically specified via an unnormalized density—by a simpler variational family. Despite its empirical successes, the theoretical properties of variational inference have only begun to be understood recently. In this talk, I will discuss recent developments in the theory of variational inference from an optimal transport perspective. In the first part, I will present our recent results on the stability and instability of mean-field variational inference (MFVI). Our main insight is simple: when the target distribution is strongly log-concave, MFVI is quantitatively stable under perturbations of the target, whereas even for simple non–log-concave targets such as a mixture of two Gaussians, MFVI provably suffers from mode collapse. The consequencs of our results are discussed, including guarantees for robust Bayesian inference and a quantitative Bernstein–von Mises theorem. In the second part of the talk, I will present our work on the statistical and computational theory for a class of structured variational inference where the variational family consists of all star-shaped distributions. We establish quantitative approximation guarantees and provide a polynomial-time algorithm for solving the VI problem when the target distribution is strongly log-concave. We also discuss concrete examples, including generalized linear models with Gaussian likelihoods. We also discuss concrete examples including generalized linear models with Gaussian likelihoods. This talk is based on joint work with Shunan Sheng, Alberto González-Sanz, Marcel Nutz, Sinho Chewi, Binghe Zhu, and Aram Pooladian.
Tuesday, January 20, 2026
Speaker: Jiequn Han (Flatiron Institute) [Zoom Link]
Title: Driftlite: Lightweight drift control for inference-time scaling of diffusion models
Abstract: We study inference-time scaling for diffusion models, where a pre-trained model is adapted to new target distributions without retraining. While guidance-based methods are simple but biased, particle-based approaches such as Sequential Monte Carlo often suffer from weight degeneracy and high computational cost. We introduce DriftLite, a lightweight, training-free particle-based method that steers inference dynamics on the fly with provably optimal stability control. DriftLite exploits a previously unexplored degree of freedom in the Fokker–Planck equation between the drift and the particle potential, leading to two practical schemes, Variance- and Energy-Controlling Guidance (VCG/ECG), which approximate the optimal drift with minimal overhead. Across Gaussian mixture models, interacting particle systems, and large-scale protein–ligand co-folding problems, DriftLite consistently reduces variance and improves sample quality compared to pure guidance and Sequential Monte Carlo baselines.
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.