From latent dynamics to data geometry: nonlinear diffusion modelling for protein structures

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DOI	Resolve DOI: https://doi.org/10.1016/j.csbj.2025.11.065
Author	Search for: Liang, Xiao¹ORCID identifier: https://orcid.org/0009-0005-2475-1890; Search for: Paquet, Eric²ORCID identifier: https://orcid.org/0000-0001-6515-2556; Search for: Viktor, Herna¹; Search for: Michalowski, Wojtek¹ORCID identifier: https://orcid.org/0000-0002-9198-6439
Affiliation	University of Ottawa National Research Council Canada. Digital Technologies
Funder	Search for: National Research Council Canada
Format	Text, Article
Subject	generative diffusion model; protein backbone generation; nonlinear stochastic differential equation; normalizing flow; likelihood-based metric
Abstract	The role and impact of nonlinearity in generative diffusion models remain largely unexplored and theoretically underdeveloped. In this work, we introduce ProT-INDM, an implicit nonlinear diffusion framework that uses invertible normalizing flows to induce nonlinear data-space dynamics from tractable latent SDEs and employs probability-flow ODEs for exact likelihood computation. This design provides a principled and flexible methodology for modelling complex protein backbone distributions, forming the first tractable modelling scheme for training nonlinear diffusion models. This general framework bridges nonlinear SDEs with score-based generative modelling, providing both theoretical insights and empirical improvements over linear diffusion model baselines.
Publication date	2025-12-02
Publisher	Elsevier B.V. Research Network of Computational and Structural Biotechnology
Copyright statement	Crown Copyright © 2025
Licence	Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) https://creativecommons.org/licenses/by-nc-nd/4.0/
In	Computational and Structural Biotechnology Journal 31, no. C (2026): 13–23.
Language	English
Peer reviewed	Yes
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Record identifier	ecfb021d-6eb7-4a6a-b160-0089ad2d4f49
Record created	2026-02-19
Record modified	2026-03-09

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Date modified:: 2026-04-17