When Can Conditional Flow Matching Replace Pointwise Negative Log-Likelihood?

תקציר מקורי באנגליתarXiv:2608.28010v2 Announce Type: replace-cross Abstract: Flow matching enables likelihood-free training, yet alignment methods increasingly reuse conditional flow matching (CFM) losses as endpoint negative log-likelihoods (NLLs) and their old/new differences as log-likelihood ratios. We characterize when these substitutions are valid. For linear Gaussian paths, we exactly decompose endpoint NLL into entropy, a weighted CFM objective, an interior velocity--score residual, and a boundary residual. Thus CFM-only estimates and differences are exact only when the corresponding residuals cancel. At the off-policy population optimum, ordinary CFM is not generally a pointwise NLL estimator, whereas \(w_{\mathrm{sc}}(t)=(1-t)/t\) removes the interior residual; this positive result does not extend