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

Xiao Liang, Eric Paquet, Herna Viktor, Wojtek Michalowski

Abstract read

In one paragraph

Article in Computational and structural biotechnology journal, 2026. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Not yet cited in PubMed.

0numbers the graph read from it

0cells of the map it votes in

0citing papers in PubMed

–field-weighted citation impact

1 · What the graph read from it

What it found

Each row is one number read from the abstract, on the scale the paper reported it, with its interval. Left of the dashed line favours the treatment, right favours the comparator. Under each row is the sentence it came from. New to these charts? A ten-minute tutorial.

The abstract states no effect estimate the extractor could read, or names no intervention and outcome on the map, so this paper lights no cell and moves no belief. It is still indexed, cited and linked below.

2 · The registry

The trial behind it

Trials whose registry record cites this paper, or whose number appears in the abstract. A trial that started after this paper was published is citing it as background, not reporting it.

Neither the registry nor the abstract names a trial number. If this is a trial report, that itself is worth knowing.

3 · Its place in the literature

Who cites it

0 citing papers in PubMed.

No citing paper in PubMed yet.

4 · The record

Corrections and comments

PubMed lists nothing against this paper. Absence here is not a guarantee, only a check that was made.

5 · Who and what money

Authors and funding

4 authors.

Xiao LiangTelfer School of Management, University of Ottawa, Ottawa, K1N 6N5, ON, Canada.

Eric PaquetNational Research Council, 1200 Montreal Road, Ottawa, K1A 0R6, ON, Canada.

Herna ViktorSchool of Electrical Engineering and Computer Science, University of Ottawa, Ottawa, K1N 6N5, ON, Canada.

Wojtek MichalowskiTelfer School of Management, University of Ottawa, Ottawa, K1N 6N5, ON, Canada.

Funding

No grant is acknowledged in the PubMed record.

6 · The paper itself

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.

Indexed as

Generative diffusion modelLikelihood-based metricNonlinear stochastic differential equationNormalizing flowProtein backbone generation

Identifiers

PMID41503270

DOI10.1016/j.csbj.2025.11.065

PMCPMC12769809

What OpenQuestion holds

Textmetadata

LicenceCC BY-NC-ND

Read underepoch 390

Registered trials

None linked

Read under generation 80e0d062 · epoch 390. Bibliography from PubMed, PubMed Central and OpenAlex; grants from NIH RePORTER; trial links from ClinicalTrials.gov; estimates, votes and beliefs from the OpenQuestion graph.