When Can Conditional Flow Matching Replace Pointwise Negative Log-Likelihood?
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 re...
| Authors | Yansen Han, Hongxin Sun, Tao Lin |
|---|---|
| Primary category | cs.LG |
| Published | 28 August 2026 |
| Last updated at source | 6 September 2026 |
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