PDE-SSM: A Spectral State Space Approach to Spatial Mixing in Diffusion Transformers
The success of vision transformers-especially for generative modeling-is limited by the quadratic cost and weak spatial inductive bias of self-attention. We propose PDE-SSM, a spatial state-space block that replaces attention with a learnable convection-diffusion-reaction partial differential equation. This operator encodes a strong spatial prior by modeling information flow via physically grounded dynamics rather than all-to-all token interactions. Solving the PDE in the Fourier domain yields global coupling with near-linear complexity of $O(N \log N)$, delivering a principled and scalable alternative to attention. We integrate PDE-SSM into a flow-matching generative model to obtain the ...
| Authors | Eshed Gal, Moshe Eliasof, Eldad Haber |
|---|---|
| Primary category | cs.LG |
| Published | 14 March 2026 |
| Last updated at source | 4 October 2026 |
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