Publications
Research papers
Non-asymptotic Convergence of Stochastic Gradient Descent in Score-based Generative Models
We analyze stochastic gradient descent for weighted denoising score matching. We derive nonconvex optimization bounds for general score parameterizations and score-approximation guarantees along training for overparameterized two-layer ReLU networks. For this architecture, these learning guarantees are combined with a Wasserstein-2 sampling analysis that accounts for early stopping, initialization, score approximation, and discretization errors, providing a way to study how these different error terms interact in the final generation bound.
Theoretical Guarantees for SMC-Guided Diffusion Sampling
We derive non-asymptotic guarantees for conditioning pretrained diffusion models with Sequential Monte Carlo (SMC). Using forward-smoothing kernels, we separate finite-particle fluctuations from errors in initialization, score approximation, numerical integration, and guidance design. Applied to several SMC-guided samplers, the framework explains how these errors propagate and why bias can persist even with infinitely many particles.
On Forgetting and Stability of Score-based Generative Models
We study how reverse-time dynamics in score-based generative models forget perturbations along the sampling trajectory. Using Harris-type arguments based on Lyapunov drift and localized minorization, we establish contraction in weighted total variation and quantify the propagation of initialization, score-approximation, and discretization errors. This provides a stability perspective in which errors introduced earlier in the reverse dynamics can have a reduced influence on the final generated distribution.
Wasserstein Convergence of Critically Damped Langevin Diffusions
We study the convergence guarantees of Critically Damped Langevin Diffusions (CLDs) for score-based generative modeling and provide, to the best of our knowledge, the first Wasserstein-2 upper bound for kinetic SGMs by analyzing the Lipschitz regularity of a modified score function. Our study also motivates the introduction of a noise–control hyperparameter that restores ellipticity by injecting noise across the entire state space. This choice has a measurable impact on generation quality in synthetic datasets.
An Analysis of the Noise Schedule for Score-based Generative Models
We study how the choice of the noise schedule impacts the generation error in Score-based Generative Models (SGMs). We derive explicit upper bounds for both the Kullback–Leibler divergence and the Wasserstein-2 distance between the generated and target distributions, highlighting their dependence on model hyperparameters and regularity of the data distribution. Theoretical findings are supported by numerical experiments on synthetic and real datasets.
Notes and expository writing
A Stochastic Analysis Perspective on Diffusion Models
We trace the probabilistic ideas behind diffusion models, from Langevin sampling and score matching to Gaussian smoothing, annealed Langevin dynamics, and reverse-time SDEs. A path-space perspective clarifies what diffusion time reversal requires beyond matching one-time marginals, with a martingale-based proof sketch. We then connect this idealized construction to practical training and sampling
You can also find my articles on my Google Scholar profile.