Co-Evolving Paths and Flows via Path-Flow Alignment
Joint path-flow training with a stochastic regularizer improves ImageNet-256 FID without changing inference.
The paper treats path-flow alignment as a joint training objective for flow matching, training an endpoint-preserving path network and a flow network with the same loss. Alignment loss alone is unreliable for path learning: path overfitting can reduce the loss while sample quality declines, associated with low-entropy bottlenecks in intermediate marginals. A stochastic path regularizer hides part of the source information while preserving endpoints and imposes an entropy floor. On ImageNet-256 with SiT backbones, the method improves FID across scales and extends to model-guidance training without changing the inference architecture or sampler.
- An endpoint-preserving path network and a flow network share one alignment loss.
- Path overfitting can lower the loss while sample quality worsens.
- Failures coincide with low-entropy bottlenecks in intermediate path marginals.
- A stochastic regularizer improves ImageNet-256 FID without changing inference.
From the original article
1 min read at arxiv.orgWe 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.
By Zeyu Michael Li · arxiv.org
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