CaLMFlow: Volterra Flow Matching using Causal Language Models

• URL: http://arxiv.org/abs/2410.05292v1
• Date: Thu, 3 Oct 2024 05:07:41 GMT
• Title: CaLMFlow: Volterra Flow Matching using Causal Language Models
• Authors: Sizhuang He, Daniel Levine, Ivan Vrkic, Marco Francesco Bressana, David Zhang, Syed Asad Rizvi, Yangtian Zhang, Emanuele Zappala, David van Dijk,
• Abstract summary: CaLMFlow is a framework that casts flow matching as a Volterra integral equation (VIE) Our method implements tokenization across space and time, thereby solving a VIE over these domains. We demonstrate CaLMFlow's effectiveness on synthetic and real-world data, including single-cell perturbation response prediction.
• Score: 14.035963716966787
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• 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.

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