Notice: The reproducibility variables underlying each score are classified using an automated LLM-based pipeline, validated against a manually labeled dataset. LLM-based classification introduces uncertainty and potential bias; scores should be interpreted as estimates. Full accuracy metrics and methodology are described in Coakley et alK. L. Coakley, T. Snelleman, H. Hoos, and O. E. Gundersen, "The embrace of open science: An analysis of a decade of AI research and 56 800 conference papers," Under Review, 2026..
On the Relation between Rectified Flows and Optimal Transport
Authors: Johannes Hertrich, Antonin Chambolle, Julie Delon
NeurIPS 2025 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | Our first contribution is a set of invariance properties of rectified flows and explicit velocity fields. In addition, we also provide explicit constructions and analysis in the Gaussian (not necessarily independent) and Gaussian mixture settings and study the relation to optimal transport. Our second contribution addresses recent claims suggesting that rectified flows... can yield (asymptotically) solutions to optimal transport problems. We study the existence of solutions for this problem and demonstrate that they only relate to optimal transport under assumptions that are significantly stronger than those previously acknowledged. In particular, we present several counterexamples that invalidate earlier equivalence results in the literature, and we argue that enforcing a gradient constraint on rectified flows is, in general, not a reliable method for computing optimal transport maps. |
| Researcher Affiliation | Academia | Johannes Hertrich Université Paris Dauphine PSL & Inria Mokaplan, Paris EMAIL Antonin Chambolle Université Paris Dauphine PSL & Inria Mokaplan, Paris EMAIL Julie Delon ENS Paris EMAIL |
| Pseudocode | No | The paper describes mathematical procedures and proofs. No structured pseudocode or algorithm blocks are present. |
| Open Source Code | No | We have only some small examples verifying our theoretical results. These examples can easily be reproduced using existing code bases like the one from [33]. |
| Open Datasets | No | The paper uses synthetically constructed distributions and samples for its numerical verifications (e.g., Gaussian distributions, shifted probability measures as defined in Section 4.1 and Remark 12). It does not provide or explicitly refer to any publicly accessible external datasets with specific links or citations for use in its experiments. |
| Dataset Splits | No | The paper uses synthetically generated data for numerical verification, not pre-existing datasets that would require explicit training/test/validation splits. |
| Hardware Specification | No | The proof-of-concept experiments in the appendix can be performed with a standard consumer workstation. |
| Software Dependencies | No | We compute the discrete optimal coupling between them using the Python Optimal Transport (POT) package [17]. |
| Experiment Setup | Yes | For the implementation, we parameterize the velocity fields v(i) t as v(i) t (x) = φ(i)(t, x), where φ(i) is a fully connected Re LU neural network with three hidden layers and 512 neurons per hidden layer. We minimize the loss functions L(v(i) t |X(i) 0 , X(i) 1 ) with the Adam optimizer for 40000 steps with batch size 256 and initial step size 10 2 which is reduced by a factor of 0.995 every 40 steps. |