One-Shot Generative Flows: Existence and Obstructions

2026-04-20 · Source: stat.ML updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Mathematics & Computational Sciences · Depth: Expert, quick

Summary

The paper "One-Shot Generative Flows: Existence and Obstructions" by Tsimpos, Sharp, and Marzouk, submitted on April 16, 2026, investigates dynamic measure transport for generative modeling. It focuses on stochastic processes X∙ whose marginals interpolate between a source distribution P0 and a target distribution P1, maintaining independence such that (X0,X1)∼P0⊗P1. The authors explore "straight-line flows," defined as processes where pointwise acceleration vanishes, making them exactly integrable by first-order methods. They provide multiple PDE-based characterizations of straightness and demonstrate a sharp dichotomy: explicit, computable straight-line processes exist for arbitrary Gaussian endpoints, but not for targets with sufficiently well-separated modes. This is supported by several impossibility theorems, revealing a fundamental link between sample-path behavior and the space-time geometry of the flow map.

Key takeaway

For research scientists developing generative models, understanding the existence and limitations of straight-line flows is critical. You should consider that while straight-line processes are feasible for Gaussian distributions, they are fundamentally impossible for targets with well-separated modes, necessitating alternative flow designs for complex multimodal data.

Key insights

Straight-line generative flows exist for Gaussian endpoints but are impossible for targets with well-separated modes.

Principles

• Endpoint independence is key.
• Straightness implies vanishing acceleration.

Method

The study characterizes straight-line flows using PDEs involving conditional statistics of the stochastic process X∙, whose conditional expectations define an ODE flow map.

In practice

• Construct straight flows for Gaussian data.
• Avoid straight flows for multimodal targets.

Topics

• Generative Flows
• Measure Transport
• Stochastic Processes
• Straight-Line Flows
• Gaussian Endpoints

Best for: Research Scientist, AI Scientist

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Editorial summary, takeaway, and curation by AIssential. Original article published by stat.ML updates on arXiv.org.