CaLMFlow: Volterra Flow Matching using Causal Language Models

TL;DR

CaLMFlow introduces a novel flow matching framework using causal language models, formulating it as a Volterra integral equation, which enhances the modeling of complex, high-dimensional data with improved scalability and context-awareness.

Contribution

It presents a new approach that leverages large language models for flow matching by casting it as a Volterra integral equation, bridging discrete language modeling with continuous data generation.

Findings

Outperforms ODE solver-dependent methods like CFM.

Effective on synthetic and real-world data, including single-cell perturbation prediction.

Incorporates textual context and generalizes to unseen conditions.

Abstract

We introduce CaLMFlow (Causal Language Models for Flow Matching), a novel framework that casts flow matching as a Volterra integral equation (VIE), leveraging the power of large language models (LLMs) for continuous data generation. CaLMFlow enables the direct application of LLMs to learn complex flows by formulating flow matching as a sequence modeling task, bridging discrete language modeling and continuous generative modeling. Our method implements tokenization across space and time, thereby solving a VIE over these domains. This approach enables efficient handling of high-dimensional data and outperforms ODE solver-dependent methods like conditional flow matching (CFM). We demonstrate CaLMFlow's effectiveness on synthetic and real-world data, including single-cell perturbation response prediction, showcasing its ability to incorporate textual context and generalize to unseen conditions. Our results highlight LLM-driven flow matching as a promising paradigm in generative modeling, offering improved scalability, flexibility, and context-awareness.