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Latent Stochastic Interpolants

ICLR 2026 Conference SubmissionAnonymous Authors
OpenReview Score: 7.3Download Report PDF
Generative ModelsStochastic InterpolantsFlow Models
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.

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This report is AI-GENERATED using Large Language Models and WisPaper (A scholar search engine). It analyzes academic papers' tasks and contributions against retrieved prior work. While this system identifies POTENTIAL overlaps and novel directions, ITS COVERAGE IS NOT EXHAUSTIVE AND JUDGMENTS ARE APPROXIMATE. These results are intended to assist human reviewers and SHOULD NOT be relied upon as a definitive verdict on novelty.
NOTE that some papers exist in multiple, slightly different versions (e.g., with different titles or URLs). The system may retrieve several versions of the same underlying work. The current automated pipeline does not reliably align or distinguish these cases, so human reviewers will need to disambiguate them manually.
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Overview

Overall Novelty Assessment

The paper introduces Latent Stochastic Interpolants (LSI), a framework for jointly learning encoder, decoder, and latent generative dynamics via stochastic interpolation. It resides in the 'Latent Stochastic Interpolants and Generative Bridges' leaf, which contains only two papers total. This is a notably sparse research direction within the broader taxonomy of 50 papers across 20 leaf nodes, suggesting the specific combination of stochastic interpolants with end-to-end latent variable learning remains relatively unexplored compared to more crowded areas like latent diffusion for static data.

The taxonomy reveals several neighboring branches: 'Diffusion Models in Latent Space' (11 papers across four sub-leaves) focuses on score-based methods in learned representations, while 'Stochastic Latent Dynamics' (5 papers) emphasizes SDE-based frameworks with variational inference. 'Flow-Based Generative Models' (2 papers) explores optimal transport flows. LSI bridges these directions by combining stochastic interpolation—a transport-inspired approach—with joint latent space optimization, distinguishing itself from standard latent diffusion's fixed encoder-decoder paradigms and from pure SDE models that lack the interpolant formulation's explicit distribution-matching guarantees.

Among 24 candidates examined, the continuous-time ELBO contribution shows overlap: 2 of 4 examined papers provide refutable prior work, indicating this theoretical component has substantial precedent within the limited search scope. The LSI framework itself (10 candidates, 0 refutations) and the unifying perspective (10 candidates, 0 refutations) appear more novel relative to the examined literature. The analysis explicitly covers top-K semantic matches plus citation expansion, not an exhaustive survey, so these statistics reflect novelty within a focused but incomplete sample of related work.

Given the sparse taxonomy leaf and limited refutations for two of three contributions, the work appears to occupy a relatively underexplored niche. However, the ELBO derivation's overlap with prior continuous-time variational methods suggests incremental theoretical refinement rather than foundational innovation in that component. The assessment is constrained by the 24-paper search scope and may not capture all relevant precedents in adjacent communities.

Taxonomy

Core-task Taxonomy Papers
50
3
Claimed Contributions
24
Contribution Candidate Papers Compared
2
Refutable Paper

Research Landscape Overview

Core task: generative modeling in latent space with continuous time dynamics. This field addresses how to learn and sample from complex data distributions by evolving latent representations through continuous-time processes. The taxonomy reveals several major branches: Continuous-Time Latent Dynamical Systems focus on neural ODEs and SDEs that model temporal evolution in learned embeddings, often applied to irregular time series or physical systems. Diffusion Models in Latent Space adapt score-based generative methods to compressed representations, balancing sample quality with computational efficiency. Latent Stochastic Interpolants and Generative Bridges construct explicit transport maps or stochastic paths between distributions, offering principled frameworks for generation and interpolation. Spatial and Graph Dynamics extend these ideas to structured data such as dynamic graphs or spatiotemporal fields, while Domain-Specific Applications demonstrate successes in areas ranging from molecular simulation to audio synthesis. Discrete-Time and Hybrid Approaches blend continuous formulations with practical discretization strategies, and Inference and Optimization Methods tackle the computational challenges of training and sampling in these models. A particularly active line of work explores how to design efficient interpolation schemes that minimize path complexity or enforce physical constraints, as seen in Path Minimizing ODEs[6] and Density Guidance Flow[4]. Another contrasting direction emphasizes flexible stochastic bridges that can handle irregular or multimodal data, exemplified by Neural Dynamics Latent SDEs[2] and ARTEMIS[11]. Latent Stochastic Interpolants[0] sits naturally within the Generative Bridges branch, proposing a framework for constructing stochastic paths in latent space that interpolate between data and noise distributions. Compared to ARTEMIS[11], which focuses on adaptive temporal modeling for irregular observations, Latent Stochastic Interpolants[0] emphasizes the design of principled interpolation dynamics that can be efficiently sampled. This work contributes to ongoing efforts to unify optimal transport perspectives with generative modeling, addressing trade-offs between theoretical guarantees, sampling speed, and the expressiveness of learned latent dynamics.

Claimed Contributions

Latent Stochastic Interpolants (LSI) framework

The authors introduce LSI, a framework that enables end-to-end joint learning of an encoder, decoder, and generative model in an unobserved latent space with continuous-time dynamics. This extends Stochastic Interpolants to support jointly optimized latent variable models, which was previously not possible since SI requires direct access to samples from both distributions.

10 retrieved papers
Principled continuous-time ELBO objective

The authors derive a novel Evidence Lower Bound (ELBO) training objective formulated directly in continuous time. This objective enables simulation-free scalable training while preserving the flexibility of arbitrary prior distributions and providing data log-likelihood control, addressing the computational challenges of applying SI in high-dimensional spaces.

4 retrieved papers
Can Refute
Unifying perspective on continuous-time latent variable models

The authors provide a theoretical perspective that unifies Stochastic Interpolants with latent variable models through continuous-time stochastic processes. This perspective connects diffusion bridges, variational posteriors, and stochastic interpolants to enable joint optimization in latent spaces.

10 retrieved papers

Core Task Comparisons

Comparisons with papers in the same taxonomy category

Contribution Analysis

Detailed comparisons for each claimed contribution

Contribution

Latent Stochastic Interpolants (LSI) framework

The authors introduce LSI, a framework that enables end-to-end joint learning of an encoder, decoder, and generative model in an unobserved latent space with continuous-time dynamics. This extends Stochastic Interpolants to support jointly optimized latent variable models, which was previously not possible since SI requires direct access to samples from both distributions.

Contribution

Principled continuous-time ELBO objective

The authors derive a novel Evidence Lower Bound (ELBO) training objective formulated directly in continuous time. This objective enables simulation-free scalable training while preserving the flexibility of arbitrary prior distributions and providing data log-likelihood control, addressing the computational challenges of applying SI in high-dimensional spaces.

Contribution

Unifying perspective on continuous-time latent variable models

The authors provide a theoretical perspective that unifies Stochastic Interpolants with latent variable models through continuous-time stochastic processes. This perspective connects diffusion bridges, variational posteriors, and stochastic interpolants to enable joint optimization in latent spaces.

Table of Contents