Uploaded August 2026 | Updated September 2026, 2 weeks ago
Jianfeng Lu (Duke University)
https://simons.berkeley.edu/talks/jianfeng-lu-duke-university-2026-08-06
Diffusion Generative Modeling: Progress and Next Steps
Let μ(dx) ∝ e^(−U(x)) dx on ℝ^d, where U is m-strongly convex and L-smooth, and denote by κ = L/m the condition number. We consider windowed thinning, an exact simulation method for the bouncy particle sampler and the coordinate Zigzag process. The method divides a trajectory into deterministic windows and uses a gradient evaluation at the beginning of each window to construct a tractable local envelope for the event rate. Combining this construction with quantitative mixing estimates and finite-time bounds on the expected numbers of bounces and flips yields query complexity guarantees from a Gaussian cold start.
For total-variation error ε, the expected query counts are O(κ^(1/2) · d · (d log κ + log(1/ε))) gradient queries for the bouncy particle sampler and O(κ · d^(1/4) · (d log κ + log(1/ε))) full-gradient equivalents for Zigzag, where d coordinate-partial queries count as one equivalent.
Jianfeng Lu (Duke University)
https://simons.berkeley.edu/talks/jianfeng-lu-duke-university-2026-08-06
Diffusion Generative Modeling: Progress and Next Steps
Let μ(dx) ∝ e^(−U(x)) dx on ℝ^d, where U is m-strongly convex and L-smooth, and denote by κ = L/m the condition number. We consider windowed thinning, an exact simulation method for the bouncy particle sampler and the coordinate Zigzag process. The method divides a trajectory into deterministic windows and uses a gradient evaluation at the beginning of each window to construct a tractable local envelope for the event rate. Combining this construction with quantitative mixing estimates and finite-time bounds on the expected numbers of bounces and flips yields query complexity guarantees from a Gaussian cold start.
For total-variation error ε, the expected query counts are O(κ^(1/2) · d · (d log κ + log(1/ε))) gradient queries for the bouncy particle sampler and O(κ · d^(1/4) · (d log κ + log(1/ε))) full-gradient equivalents for Zigzag, where d coordinate-partial queries count as one equivalent.
