Co-Evolving Paths and Flows via Path-Flow Alignment

Key points

• Instead of fixing the interpolation path and learning only the velocity field, we jointly train an endpoint-preserving path network and a flow network using the same alignment loss: the flow learns to match the path velocity, and the path learns to align its velocity to the current flow.1
• We identify path overfitting, a failure mode in which the alignment loss decreases while sample quality worsens.1
• We find that this failure is associated with low-entropy bottlenecks in the induced probability path, where the learned path routes samples through overly concentrated intermediate marginals.1
• Motivated by this diagnosis, we introduce a stochastic path regularizer that hides part of the source information from the path network while preserving exact endpoints.1

Sources (1)

• [1]Co-Evolving Paths and Flows via Path-Flow Alignment
  arXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 6, 05:24 PM

  We study path-flow alignment as a unified training objective for flow matching.

  Instead of fixing the interpolation path and learning only the velocity field, we jointly train an endpoint-preserving path network and a flow network using the same alignment loss: the flow learns to match the path velocity, and the path learns to align its velocity to the current flow.

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