Session: Technical Session I

Date & Time: Friday, May 22 — 11:00 AM–12:30 PM

Talk Title

Manifold-Aligned Generative Transport

Abstract

High-dimensional generative modeling requires a delicate balance between support fidelity—keeping generated data precisely on the data manifold—and sampling efficiency. While diffusion models capture manifold structures well, their iterative denoising steps are slow and can leak off-support. Conversely, normalizing flows offer rapid, one-pass sampling but are limited by strict invertibility constraints.

In this talk, we introduce MAGT (Manifold-Aligned Generative Transport), a novel flow-like generator that achieves the best of both worlds. MAGT learns a one-shot, manifold-aligned transport from a low-dimensional base distribution directly to the data space. By training at a fixed, numerically stable Gaussian smoothing level and approximating the score via latent anchor points, we create a tractable objective without sacrificing speed. We will demonstrate how MAGT samples in a single forward pass, tightly concentrates probability on the learned support, and enables principled likelihood evaluation. We will also share theoretical Wasserstein bounds and empirical results showing significant improvements in both fidelity and sampling speed over standard diffusion models.

This is joint work with Xinyu Tian at the University of Minnesota.