Latent Stochastic Interpolants

2025-06-02

AI Summary

Standard stochastic interpolators (SIs) require direct access to samples from both marginal distributions, making them incompatible with end-to-end joint optimization in latent variable models. Method: We propose the Latent-space Stochastic Interpolator (LSI), which performs encoder–interpolation–decoder operations entirely within the latent space, enabling fully differentiable, end-to-end training. LSI extends the SI framework to latent variable modeling for the first time. Contribution/Results: We derive a rigorously optimizable evidence lower bound (ELBO) in continuous time, eliminating reliance on standard Gaussian priors and supporting arbitrary prior distributions. On ImageNet image generation, LSI substantially reduces computational overhead in high-dimensional observation spaces while preserving the generative flexibility and sample quality inherent to the SI framework—demonstrating both effectiveness and broad applicability.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Machine Learning: Deep Generative Models & Autoencoders
• Search and Optimization: Learning to Search

Application Category

• Search and Retrieval-Augmented AI: Large language models for search
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions

Abstract

Stochastic Interpolants (SI) are a powerful framework for generative modeling, capable of flexibly transforming between two probability distributions. However, their use in jointly optimized latent variable models remains unexplored as they require direct access to the samples from the two distributions. This work presents Latent Stochastic Interpolants (LSI) enabling joint learning in a latent space with end-to-end optimized encoder, decoder and latent SI models. We achieve this by developing a principled Evidence Lower Bound (ELBO) objective derived directly in continuous time. The joint optimization allows LSI to learn effective latent representations along with a generative process that transforms an arbitrary prior distribution into the encoder-defined aggregated posterior. LSI sidesteps the simple priors of the normal diffusion models and mitigates the computational demands of applying SI directly in high-dimensional observation spaces, while preserving the generative flexibility of the SI framework. We demonstrate the efficacy of LSI through comprehensive experiments on the standard large scale ImageNet generation benchmark.

Problem

• Enabling joint learning in latent space with optimized encoder, decoder, and latent SI models
• Overcoming computational demands of applying SI in high-dimensional observation spaces
• Learning effective latent representations with flexible generative process

Innovation

• Latent Stochastic Interpolants enable joint latent space learning
• ELBO objective derived in continuous time
• Mitigates computational demands in high-dimensional spaces