Reproduce “Learning Stationary Markov Processes with Contrastive Adjustment” on OpenResearch

About this paper

Ludvig Bergenstråhle, Jens Lagergren, Joakim Lundeberg

Researchers from KTH Royal Institute of Technology and SciLifeLab developed "contrastive adjustment," an optimization algorithm for training Markov transition kernels to achieve a stationary distribution matching input data by enforcing detailed balance. This method supports flexible generative modeling, demonstrated by competitive FID scores (e.g., 18.27 on CIFAR-10, 9.40 on LSUN Church) and strong performance in interactive variant generation and inpainting on image datasets.

Key insights

• The core insight of contrastive adjustment is to enforce the detailed balance criterion, ensuring the learned Markov chain's stationary distribution matches the target data distribution, which enables local data manifold exploration.
• For practical gradient-based optimization, the training reduces to a simple update rule based solely on the gradient of the log-probability of the backward transition.
• The use of 'noise kernels,' inspired by noise-annealed sampling, enables efficient de novo sample generation by modeling data over multiple noise levels, allowing a trade-off between mixing speed and sample fidelity.

Summary by alphaXiv.