Changing the DenseAM kernel from the standard Gaussian kernel to the KDE-optimal Epanechnikov kernel results in 1) exponential capacity without the exponential and 2) meaningful, emergent memories.

Energy Matching unifies flow matching and energy-based models in a single time-independent scalar field, enabling efficient transport from noise to data while retaining explicit likelihood information for flexible, high-quality generation.

We train an energy-based model on image datasets through a dual score matching objective and analyze the local geometry of the learned energy landscape.