Mechanism works
2026
Transport-Signature Density Decoder
Replace a pixelwise density decoder with a decoder that predicts coefficients of a transport potential relative to a fixed reference density. The reconstructed density is the pushforward of the reference measure through a differentiable transport map, so positivity and total mass are structural properties rather than learned penalties.
Paper: Structure-Preserving Reduced-Order Modeling via Low-Rank Transport Signatures
arXiv:2607.01696