{"slug": "cat-flow-curvature-adaptive-steps-for-flow-matching", "title": "CAT-Flow: Curvature-Adaptive sTeps for Flow Matching", "summary": "Researchers propose two training-free algorithms, CAT-OV and CAT-OT, that adapt step-sizes at inference time for Flow Matching generative models, reducing the number of generation steps needed for comparable image quality by up to 40% across four text-to-image models. The methods, based on a connection between Flow Matching sampling and gradient flow, require no additional neural function evaluations and have truncation error bounds of constant order.", "body_md": "arXiv:2609.01746v1 Announce Type: new\nAbstract: Flow Matching has emerged as a leading framework for generative modeling, powering state-of-the-art systems such as FLUX and Stable Diffusion 3.5. However, the iterative nature of its ODE-based sampling process creates a fundamental efficiency bottleneck: the quality of generated samples is highly sensitive to the choice of step-sizes, and current models typically require 20 to 30 steps for good quality. In this work, we propose two lightweight, training-free algorithms, CAT-OV and CAT-OT that adapt step-sizes at inference time based on a novel connection between Flow Matching sampling and gradient flow. Our algorithms are computed efficiently by not requiring additional neural function evaluations. Specifically, CAT-OT estimates curvature over time via a finite-difference approximation of the time-derivative of the vector field, while CAT-OV approximates curvature over the state space via a gradient of the vector field. Under suitable conditions, both methods have truncation error bounds of constant order. Empirically, CAT-OV and CAT-OT outperform existing step-size heuristics in image quality metrics across four text- to-image Flow Matching models, reducing the number of generation steps required to reach comparable quality by up to 40%.", "url": "https://wpnews.pro/news/cat-flow-curvature-adaptive-steps-for-flow-matching", "canonical_source": "https://arxiv.org/abs/2609.01746", "published_at": "2026-09-03 04:00:00+00:00", "updated_at": "2026-09-03 04:23:24.107330+00:00", "lang": "en", "topics": ["machine-learning", "generative-ai", "ai-research"], "entities": ["arXiv", "FLUX", "Stable Diffusion 3.5"], "alternates": {"html": "https://wpnews.pro/news/cat-flow-curvature-adaptive-steps-for-flow-matching", "markdown": "https://wpnews.pro/news/cat-flow-curvature-adaptive-steps-for-flow-matching.md", "text": "https://wpnews.pro/news/cat-flow-curvature-adaptive-steps-for-flow-matching.txt", "jsonld": "https://wpnews.pro/news/cat-flow-curvature-adaptive-steps-for-flow-matching.jsonld"}}