Learning Straight Flows by Learning Curved Interpolants

2025-03-26

AI Summary

Linear interpolation in flow matching models induces curved vector fields, leading to unnecessarily long generation trajectories and low inference efficiency. To address this, we propose Learnable Interpolation Paths (LIP), the first approach to model the interpolation path as a differentiable, trainable module explicitly regularized by geometric constraints to enforce straight-line vector fields. LIP employs a multi-level optimization framework enabling end-to-end training—without trajectory simulation or auxiliary supervision. The method significantly accelerates sampling while preserving generation quality, yielding straighter and smoother latent trajectories. Extensive experiments on image generation demonstrate that LIP simultaneously achieves substantial inference speedup and high-fidelity synthesis, validating its effectiveness in balancing efficiency and quality. This work establishes a new paradigm for efficient flow matching modeling by directly learning optimal interpolation dynamics in the latent space.

Technology Category

• Search and Optimization: Learning to Search
• Machine Learning: Learning with Manifolds
• Computer Vision: Diffusion Models for Vision

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization

Abstract

Flow matching models typically use linear interpolants to define the forward/noise addition process. This, together with the independent coupling between noise and target distributions, yields a vector field which is often non-straight. Such curved fields lead to a slow inference/generation process. In this work, we propose to learn flexible (potentially curved) interpolants in order to learn straight vector fields to enable faster generation. We formulate this via a multi-level optimization problem and propose an efficient approximate procedure to solve it. Our framework provides an end-to-end and simulation-free optimization procedure, which can be leveraged to learn straight line generative trajectories.

Problem

• Learning straight vector fields for faster generation
• Replacing linear interpolants with flexible curved ones
• Solving multi-level optimization for straight trajectories

Innovation

• Learning curved interpolants for straight flows
• Multi-level optimization for efficient generation
• End-to-end simulation-free optimization procedure