CaLMFlow: Volterra Flow Matching using Causal Language Models (2410.05292v1)

Abstract: We introduce CaLMFlow (Causal LLMs for Flow Matching), a novel framework that casts flow matching as a Volterra integral equation (VIE), leveraging the power of 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 LLMing 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.

• The paper introduces CaLMFlow, recasting flow matching as a sequence modeling task using causal language models and Volterra integral equations for enhanced numerical stability.
• It enables natural language-conditioned generation, outperforming traditional ODE-based methods in scalability and robustness for complex high-dimensional data.
• Empirical evaluations show superior performance on metrics like MMD and 2-Wasserstein distance, demonstrating effectiveness in single-cell generation and synthetic dataset tasks.

Insights into CaLMFlow: Volterra Flow Matching Leveraging Causal LLMs

The paper presents CaLMFlow, an innovative approach that integrates causal LLMs (CLMs) with flow matching using Volterra integral equations (VIEs). This approach capitalizes on the capabilities of LLMs for continuous data generation, offering a robust framework that harmonizes discrete LLMing with continuous generative modeling. The primary contribution lies in recasting flow matching as a sequence modeling task, enhancing scalability and efficiency in handling high-dimensional data without the drawbacks of traditional ODE-dependent methods like Conditional Flow Matching (CFM).

Key Contributions

1. Volterra Flow Matching Framework: CaLMFlow employs VIEs for modeling flow matching, utilizing CLMs to approximate solutions. This methodology enhances numerical stability and performance over traditional ODE-based approaches, addressing issues like stiffness and computational expense that typically plague ODE systems.
2. Natural Language Conditions for Generation: The framework allows for controllable flow generation using natural language prompts. This capability is particularly beneficial for applications like single-cell perturbation response prediction, where textual prompts can condition the generative process, outperforming other strategies in scalability and flexibility.
3. Variational Decoding for Continuous Tokens: By extending LLMing techniques into continuous domains, CaLMFlow introduces variational decoding, which facilitates the sampling and generation of continuous data. An ablation paper underscores its importance in accurately modeling continuous data.
4. Spatiotemporal and Multi-Trajectory Tokenization: Incorporating spatiotemporal tokenization, the model effectively captures correlations between spatial and temporal domains. Furthermore, the capability to model multiple trajectories concurrently significantly enhances performance, as evidenced by experiments on synthetic datasets.

Empirical Evaluation

CaLMFlow was tested against synthetic datasets for validating its potential in high-dimensional environments. It showed superior robustness to traditional ODE approaches, maintaining strong performance where others falter. The real-world applicability was demonstrated in single-cell generation tasks, where CaLMFlow not only matched but surpassed existing methods on key metrics like maximum mean discrepancy (MMD) and 2-Wasserstein distance.

In the domain of single-cell perturbation response prediction, CaLMFlow's ability to utilize natural language understanding through pretrained weights of the CLM provides additional accuracy. This model generates realistic data distributions even in unseen conditions, significantly outperforming CFM variants and other state-of-the-art single-cell generative models.

Implications and Future Directions

The approach outlined in CaLMFlow opens several avenues for applications in AI. By bridging LLMs with flow matching tasks through VIEs, this research offers promising insights into more stable and flexible modeling paradigms that are capable of handling complex and high-dimensional datasets. The integration with textual contexts also introduces a new level of applicability across multimodal generative tasks.

Looking forward, the theoretical extensions of CaLMFlow, especially the formalization of its multi-trajectory approach over function spaces and its potential use as an iterative solver, suggest an exciting frontier for research. These developments would potentially widen its scope in modeling intricate systems with complicated dynamics, pushing the boundaries of what is achievable with generative modeling frameworks.

In conclusion, CaLMFlow presents a compelling method that aligns the strengths of CLMs with the necessities of solving complex flow matching problems, providing a robust, scalable, and nuanced approach to generative modeling.