Multimarginal generative modeling with stochastic interpolants
Michael S. Albergo, Nicholas M. Boffi, Michael Lindsey, Eric, Vanden-Eijnden
TL;DR
This paper introduces a multimarginal generative modeling framework using stochastic interpolants, enabling the learning of joint distributions with multi-way correspondences among given marginals, with applications in style transfer and fairness.
Contribution
It generalizes stochastic interpolant methods to multimarginal settings, allowing efficient learning of joint distributions and extraction of multi-way correspondences.
Findings
Effective algorithms for multimarginal generative modeling.
Ability to extract multi-way correspondences among marginals.
Reduced transport cost in two-marginal cases.
Abstract
Given a set of probability densities, we consider the multimarginal generative modeling problem of learning a joint distribution that recovers these densities as marginals. The structure of this joint distribution should identify multi-way correspondences among the prescribed marginals. We formalize an approach to this task within a generalization of the stochastic interpolant framework, leading to efficient learning algorithms built upon dynamical transport of measure. Our generative models are defined by velocity and score fields that can be characterized as the minimizers of simple quadratic objectives, and they are defined on a simplex that generalizes the time variable in the usual dynamical transport framework. The resulting transport on the simplex is influenced by all marginals, and we show that multi-way correspondences can be extracted. The identification of such…
Peer Reviews
Decision·ICLR 2024 poster
The work proposes a theoretically sound and practical approach based on stochastic interpolants for the multimarginal setting. The overall proposed scheme is mathematically sound and computationally more feasible than existing schemes. Extensive experiments are performed to illustrate the idea and different scenarios of the proposed method.
The overall algorithm of the proposed method might not be very clear or easy to follow, especially for mathematically less mature audience. I suggest the authors add the pseudocode of the main algorithm to improve clarity.
- *Innovative Generative Model*: The paper's proposition of a vector-field-based generative model that utilizes a generalized form of stochastic interpolant to generate from multiple marginals is unique and intriguing. - *Optimal Path Identification*: By minimizing the Wasserstein-2 metric, the methodology seeks the most efficient path for transitions, with theoretical groundings. - *Barycentric Stochastic Interpolant*: The use of a barycentric stochastic interpolant offers a nuanced approach, e
- *Ambiguous Interpretation*: The paper does not provide a clear semantic understanding of the paths between distributions, making it difficult to ascertain the practical implications or the broader relevance of the methodology. Also, what does multi-marginal optimal transport path mean for image generation? Does it lead to better quality? In this paper, it is not answered. - *Unknown Utility*: There's a lack of clarity on the potential use-cases for this generative model. For instance, if it's
1. by lifting alpha to high-dimensional vector, the work enables to solve (K,2) marginal transport problems using only K marginal vector fields. 2. the overall presentation is clear and the empirical experiments are comprehensive.
Optimizing the vector field on simplex alpha may require delicate parameterizions. It would be better if it is more connected optimal transport. The theories look like a na\"ive extension from the work of "Stochastic Interpolants: A Unifying Framework for Flows and Diffusions". The authors can kindly point out some innovations if I may miss some key points. Section 2.2 may need some proper rewriting to be more clear.
Videos
Taxonomy
TopicsMarkov Chains and Monte Carlo Methods · Generative Adversarial Networks and Image Synthesis