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

Area of Science:

• Machine Learning
• Computational Biology
• Generative Models

Background:

• Nonlinearity in generative diffusion models is underexplored.
• Existing models often rely on linear dynamics, limiting their ability to capture complex data distributions.

Purpose of the Study:

• Introduce ProT-INDM, an implicit nonlinear diffusion framework.
• Enable principled and flexible modeling of complex protein backbone distributions.
• Bridge nonlinear stochastic differential equations (SDEs) with score-based generative modeling.

Main Methods:

• Utilizes invertible normalizing flows to induce nonlinear data-space dynamics.
• Employs tractable latent SDEs for underlying dynamics.
• Uses probability-flow ordinary differential equations (ODEs) for exact likelihood computation.

Main Results:

• Forms the first tractable modeling scheme for training nonlinear diffusion models.
• Demonstrates empirical improvements over linear diffusion model baselines.
• Provides theoretical insights into the role of nonlinearity.

Conclusions:

• ProT-INDM offers a principled and flexible approach to nonlinear diffusion modeling.
• This framework advances generative modeling for complex biological data.
• The study opens new avenues for research in nonlinear generative models.