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One-Shot Generative Flows: Existence and Obstructions

Scientific Achievement

We examine the question of if and when it is possible to construct a class of machine learning models that perform "inference" with minimal cost.
By using novel constructions and analysis, we make progress on a problem faced across a wide swath of research into and application of generative models.

Significance and Impact

Generative flows, a class of "dynamic" machine learning models, are often considered expensive due to the necessity of multiple model evaluations for each generated sample.
We address the question of existence of a one-shot flow, i.e., when we only need a single model evaluation for generating a sample.
We construct closed-form solutions for the arbitrary Gaussian case, which creates a nontrivial and counterintuitive solution that adapts methods in existing literature.
We show that it is impossible to achieve these flows for common generative flows.

Technical Approach

We discuss the case of flow-matching and stochastic interpolants with independent endpoints, i.e., the common case of training a model with independent samples of the two endpoint distributions.
We show that the affine interpolant setup, typical of flow-matching, cannot possibly give a one-shot flow with independent endpoints.
We have topological proofs of the one-shot flows' non-existence in certain high-dimensional regimes, and can show analytical rates in one-dimension for a broader class of target distributions.

PI(s)/Facility Lead(s): Youssef Marzouk

Collaborating Institutions: Massachusetts Institute of Technology,

ASCR Program: SciDAC Institutes, FASTMath

ASCR PM: Xujing Davis

Publication for this work: Tsimpos, Sharp, Marzouk. “One-Shot Generative Flows: Existence and Obstructions” Preprint (2026). doi: 10.48550/arXiv.2604.15439

Energy.gov/science

POC:�Daniel Sharp, dannys4@mit.edu

Youssef M Marzouk, dannys4@mit.edu

TALKING POINTS:

Sampling from complex probability distributions is a core task across science and engineering. It underlies weather forecasting, drug discovery, risk analysis, signal processing, and many modern data-analysis tools, so faster and more reliable sampling methods can have broad impact.
Today, many of these computational methods are slowed by repeated simulation steps. If distributions can instead be transformed along simpler "straight-line" paths, generating samples may require far fewer calculations, reducing time, energy use, and computing cost.
These efficiency gains are especially important for uncertainty quantification, which depends on drawing many realistic scenarios. Governments, laboratories, and industry rely on this capability for infrastructure planning, national security, climate resilience, and engineering design.
This paper shows that some transformations can be achieved in one exact step, while others fundamentally cannot. That distinction helps identify which problems admit simple efficient solutions and which inherently require more sophisticated multi-step approaches.
The broader significance is a roadmap for future sampling and simulation methods. By clarifying when simple transport is possible, the work can guide faster approaches in uncertainty quantification, Bayesian inference, scientific computing, and related data-driven modeling.

METADATA:

Name of the associated awarded project: FASTMath SciDAC Institute

Overall Project PI name(s): Carol Woodward (LLNL)

CITATIONS:�Tsimpos, Sharp, Marzouk. “One-Shot Generative Flows: Existence and Obstructions” Preprint (2026). doi: 10.48550/arXiv.2604.15439