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ODE-free Neural Flow Matching for One-Step Generative Modeling

arXiv:2604.06413v1 Announce Type: new Abstract: Diffusion and flow matching models generate samples by learning time-dependent vector fields whose integration transports noise to data, requiring tens to hundreds of network evaluations at inference. We instead learn the transport map directly. We propose Optimal Transport Neural Flow Matching (OT-NFM), an ODE-free generative framework that parameterizes the flow map with neural flows, enabling true one-step generation with a single forward pass. We show that naive flow-map training suffers from mean collapse, where inconsistent noise-data pairings drive all outputs toward the data mean. We prove that consistent coupling is necessary for non-degenerate learning and address this using optimal transport pairings with scalable minibatch and online coupling strategies. Experiments on synthetic benchmarks and image generation tasks (MNIST and CIFAR-10) demonstrate competitive sample quality while reducing inference to a single network evalua

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Xiao Shou · · 1 min read · 21 views
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arXiv:2604.06413v1 Announce Type: new Abstract: Diffusion and flow matching models generate samples by learning time-dependent vector fields whose integration transports noise to data, requiring tens to hundreds of network evaluations at inference. We instead learn the transport map directly. We propose Optimal Transport Neural Flow Matching (OT-NFM), an ODE-free generative framework that parameterizes the flow map with neural flows, enabling true one-step generation with a single forward pass. We show that naive flow-map training suffers from mean collapse, where inconsistent noise-data pairings drive all outputs toward the data mean. We prove that consistent coupling is necessary for non-degenerate learning and address this using optimal transport pairings with scalable minibatch and online coupling strategies. Experiments on synthetic benchmarks and image generation tasks (MNIST and CIFAR-10) demonstrate competitive sample quality while reducing inference to a single network evaluation.

Executive Summary

This article introduces Optimal Transport Neural Flow Matching (OT-NFM), an innovative ODE-free generative framework designed to overcome the computational burden of multi-step diffusion and flow matching models. By directly parameterizing the transport map from noise to data using neural flows, OT-NFM achieves true one-step generation, requiring only a single network evaluation at inference. The authors rigorously identify and address the 'mean collapse' problem inherent in naive flow-map training, proving the necessity of consistent noise-data coupling and implementing optimal transport pairings through scalable minibatch and online strategies. Experimental results on synthetic and image generation tasks (MNIST, CIFAR-10) demonstrate competitive sample quality alongside significant inference efficiency gains.

Key Points

  • ▸ Introduces Optimal Transport Neural Flow Matching (OT-NFM) for one-step generative modeling.
  • ▸ Directly parameterizes the transport map from noise to data using neural flows, eliminating ODE integration.
  • ▸ Identifies and provides a theoretical proof for the 'mean collapse' problem in naive flow-map training.
  • ▸ Resolves mean collapse by employing optimal transport (OT) for consistent noise-data pairings, using scalable minibatch and online coupling.
  • ▸ Achieves competitive sample quality on benchmarks (MNIST, CIFAR-10) with a single network evaluation at inference.

Merits

Significant Inference Efficiency

Reduces generative inference from tens/hundreds of steps to a single forward pass, a substantial improvement for real-time applications.

Theoretical Rigor

Provides a formal proof for the 'mean collapse' phenomenon, grounding the proposed solution in solid mathematical understanding.

Novel Problem Formulation

Directly learning the transport map is a distinct and promising approach compared to learning vector fields for ODE integration.

Scalable OT Implementation

The use of minibatch and online optimal transport strategies addresses the computational challenges typically associated with OT in high-dimensional settings.

Demerits

Complexity of OT Computation

While scalable, optimal transport still introduces computational overhead during training, which might be significant for very large datasets or complex distributions.

Limited Generative Diversity (Potential)

Directly mapping noise to data might, in some complex scenarios, struggle to capture the full multi-modality of a distribution as effectively as iterative refinement methods, though the paper's results are promising.

Benchmarking Scope

Experiments are conducted on MNIST and CIFAR-10. Performance on higher-resolution images and more complex datasets (e.g., ImageNet) would provide a more comprehensive evaluation of scalability and quality.

Expert Commentary

The article by B. et al. presents a compelling advancement in generative modeling, skillfully pivoting from the prevalent paradigm of learning vector fields for iterative refinement to directly learning the optimal transport map. The theoretical identification and resolution of 'mean collapse' is particularly noteworthy, demonstrating a deep understanding of the underlying mathematical challenges. This rigorous foundation elevates OT-NFM beyond a mere heuristic optimization. The true value proposition lies in the substantial reduction in inference cost without a commensurate drop in sample quality, a holy grail for many real-world AI applications. While the current benchmarking is modest, the conceptual shift is profound. Future work should aggressively explore its performance on high-dimensional, complex datasets and investigate potential trade-offs between one-step generation and the nuanced control offered by multi-step processes. This work sets a new benchmark for inference efficiency in generative models, challenging the prevailing architectural assumptions.

Recommendations

  • ✓ Conduct extensive evaluations on larger, more complex datasets (e.g., ImageNet, high-resolution video) to thoroughly assess scalability and fidelity.
  • ✓ Explore hybrid approaches that combine the efficiency of OT-NFM with the fine-grained control or diversity enhancement capabilities of multi-step models.
  • ✓ Investigate the interpretability of the learned transport maps, potentially revealing new insights into data manifold structures.
  • ✓ Develop and benchmark more advanced optimal transport approximation techniques to further reduce training complexity without sacrificing coupling consistency.

Sources

Original: arXiv - cs.LG

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