BézierFlow optimizes the sampling trajectory to achieve a 2–3× performance improvement for few-step generation with ≤ 10 NFEs. As illustrated in the figure below, BézierFlow closely follows the sampling trajectory of the high-NFE teacher using only 3 NFEs. Training takes only ~15 minutes!
We introduce BézierFlow, a lightweight training approach for few-step generation with pretrained diffusion and flow models. BézierFlow achieves a 2–3× performance improvement for sampling with ≤ 10 NFEs while requiring only 15 minutes of training.
Recent lightweight training approaches have shown promise by learning optimal timesteps, but their scope remains restricted to ODE discretizations. To broaden this scope, we propose learning the optimal transformation of the sampling trajectory by parameterizing stochastic interpolant (SI) schedulers. The main challenge lies in designing a parameterization that satisfies critical desiderata, including boundary conditions, differentiability, and monotonicity of the SNR.
To effectively meet these requirements, we represent scheduler functions as Bézier functions, where control points naturally enforce these properties. This reduces the problem to learning an ordered set of points in the time range, while the interpretation of the points changes from ODE timesteps to Bézier control points. Across a range of pretrained diffusion and flow models, BézierFlow consistently outperforms prior timestep-learning methods, demonstrating the effectiveness of expanding the search space from discrete timesteps to Bézier-based trajectory transformations.
For pretrained diffusion and flow models, BézierFlow consistently produces sharper details and fewer artifacts at low NFEs compared to baselines across various solvers and datasets.
BézierFlow consistently achieves significantly lower FID scores compared to base solvers across various diffusion and flow models, demonstrating the effectiveness of Bézier-based trajectory transformations at low NFEs.
BézierFlow is a generic framework applicable not only to image generation but also to various generative tasks, such as 3D point cloud generation and layout generation.
Our goal is to optimize a target path (student) that achieves high-quality generation with few NFEs by mimicking a source path (teacher) that uses many steps. We formulate this as a teacher-forcing objective:
where \(\xi\) and \(\bar{\xi}_\theta\) are the teacher (\(N\) steps) and student (\(M\) steps) solvers, respectively, and \(M \ll N\).
We propose BézierFlow, which parameterizes the target scheduler \((\bar\alpha^\theta_s, \bar\sigma^\theta_s)\) using Bézier curves. We relate the target and source schedulers via a scaling reparameterization \(\bar{x}_s = c_s x_{t_s}\), where:
This ensures smoothness (\(C^2\) continuity) and allows for analytic computation of the transformed velocity field:
This Bézier-based parameterization enables stable optimization of the sampling trajectory while preserving the endpoint marginals, effectively minimizing dicretization error of few-step generation.
There are a lot of excellent works that are related to BézierFlow:
UniPC: A Unified Predictor-Corrector Framework for Fast
Sampling of Diffusion Models, NeurIPS 2023
Fast Sampling of Diffusion Models with Exponential Integrator, ICLR
2023
Accelerating Diffusion Sampling with Optimized Time Steps, CVPR
2024
On the Trajectory Regularity of ODE-Based Diffusion Sampling, ICML
2024
Bespoke Solvers for Generative Flow Models, ICLR 2024
Learning to Discretize Denoising Diffusion ODEs, ICLR 2025
We use the following pretrained diffusion and flow models provided by:
@article{min:2025bezierflow,
title={B\'ezierFlow: Learning B\'ezier Stochastic Interpolant Schedulers for Few-Step Generation},
author={Min, Yunhong and Koo, Juil and Yoo, Seungwoo and Sung, Minhyuk},
journal={arXiv preprint arXiv:2512.13255},
year={2025}
}