Latent Stochastic Interpolants

arXiv stat.ML / 4/23/2026

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Key Points

The paper introduces Latent Stochastic Interpolants (LSI) as an extension of Stochastic Interpolants that enables interpolation/generation between two distributions within a learned latent space.
Unlike prior SI approaches that require direct access to samples from both distributions, LSI uses end-to-end optimization of an encoder, a decoder, and a latent SI model.
The method is grounded in a continuous-time formulation that derives a principled Evidence Lower Bound (ELBO) objective for joint learning.
By operating in latent space, LSI reduces the computational burden of applying SI to high-dimensional observation data while retaining SI’s generative flexibility.
The authors validate LSI with extensive experiments on the large-scale ImageNet generation benchmark, showing strong performance.

Abstract

Stochastic Interpolants (SI) is a powerful framework for generative modeling, capable of flexibly transforming between two probability distributions. However, its use in jointly optimized latent variable models remains unexplored as it requires 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.