Beyond the Manifold Hypothesis: Hybrid Spectral Parameterizations for Flow Matching
Flow matching and diffusion can be trained to predict different quantities, most commonly the data $x_1$, the source noise $x_0$, or the velocity~$v$. Although theoretically equivalent, these can lead to substantially different performances. We identify two main drivers for these differences: the source--data signal-to-noise ratio, and the information bottleneck induced by the neural architecture. We show that, beyond intrinsic data dimension, the factor affecting the optimal parametrization the most is a certain signal-to-noise ratio in each data covariance direction. From this analysis, we introduce new \emph{spectral hybrid} parameterizations that adapt across time and data covariance ...
| Authors | Ségolène Martin, Anne Gagneux, Quentin Bertrand et al. |
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| Primary category | cs.LG |
| Published | 26 September 2026 |
| Last updated at source | 26 September 2026 |
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