Drifting Fields are not Conservative
Drifting models have recently gained attention for generating high-quality samples in a single forward pass. During training, they learn a push-forward map by following a vector-valued field, the drift field. We ask whether this procedure is equivalent to optimizing a scalar loss and find that, in general, it is not: drift fields are not conservative and cannot be written as the gradient of any scalar potential. We identify the position-dependent normalization as the source of non-conservatism, with the Gaussian kernel as the unique radial exception. Guided by this, we introduce the sharp kernel $k^\#$ and a sharp-normalized drift field that is conservative for general radial kernels. The...
| Authors | Leonard T. Franz, Sebastian Hoffmann, Tim Weiland et al. |
|---|---|
| Primary category | cs.LG |
| Published | 7 April 2026 |
| Last updated at source | 8 May 2026 |
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