Latent Process Generator Matching

2026-05-21 · Source: stat.ML updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Mathematics & Computational Sciences · Depth: Expert, extended

Summary

Latent Process Generator Matching introduces a general framework that treats the observed generative state X_t as a deterministic image Φ(Y_t) of a tractable Markov process Y_t. This framework generalizes existing Generator Matching theory by allowing conditioning on time-dependent latent Markov processes, rather than just static variables. It demonstrates that one can learn the generator of a stochastic process on the image space, which possesses the same one-time marginal distributions as the projected process. This approach subsumes prior work like Edit Flows, OneFlow, Flowception, and Branching Flows, which previously relied on case-by-case projection results often limited to discrete latent components. The framework provides a general loss function and a gradient equality theorem (Theorem 3.12) that justifies training a neural network against conditional targets to recover the correct marginal generator. A concrete application for protein structure generation with manifold-valued latents is also outlined.

Key takeaway

For machine learning engineers developing generative models, this framework simplifies handling complex latent processes. You can now train models using auxiliary time-dependent latent dynamics, even if those dynamics are intractable at generation time or not part of the final output. This allows for more flexible model architectures and broader application, such as protein structure generation, by providing a unified theoretical basis for conditional training.

Key insights

Latent Process Generator Matching generalizes generative models by learning from time-dependent, projected latent Markov processes.

Principles

• Observed state is image of tractable Markov process.
• Conditional loss training recovers marginal generator.
• Generalizes static latent variable conditioning.

Method

The framework defines a conditional generator L_t^y_t and a conditional linear parametrisation F_t^y_t(Φ(y_t)). Training a neural network F_t^θ(x_t) against a Bregman divergence loss L_cgm(θ) recovers the marginal generator.

In practice

• Enables new flow matching schemes.
• Supports protein structure generation.
• Integrates discrete and continuous latents.

Topics

• Latent Process Generator Matching
• Generative Models
• Flow Matching
• Diffusion Models
• Markov Processes
• Protein Structure Generation

Best for: Research Scientist, AI Scientist, Machine Learning Engineer

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Editorial summary, takeaway, and curation by AIssential. Original article published by stat.ML updates on arXiv.org.