Co-Evolving Interpolants and Flows via Path-Flow Alignment

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. Although every fixed learned path defines a valid flow-matching objective, the alignment loss alone is not a reliable criterion for path learning. We identify *path overfitting*, a failure mode in which the alignment loss decreases while sample quality worsens. We trace this failure to low-entropy bottlenecks in the induced probability path, where the learned interpolant routes samples through overly concentrated intermediate marginals. 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. The resulting regularized objective controls entropy collapse and makes joint path--flow training effective. On ImageNet-$256\times256$ with SiT backbones, our method consistently improves FID across model scales, extends to model-guidance training, and leaves the inference-time architecture and sampler unchanged. Code is available at https://anonymous.4open.science/r/traj_opt_paper-4D80.