# B'ezierFlow: Learning B'ezier Stochastic Interpolant Schedulers for Few-Step Generation

arXiv: https://arxiv.org/abs/2512.13255 · HTML: https://mlsanity.com/paper/2512.13255/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 37 of its 42 references that are in the map.
- First posted on arXiv 15 Dec 2025.

## Builds on (most cited first, 30 of 37)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [CLIPScore: A Reference-free Evaluation Metric for Image Captioning](https://mlsanity.com/paper/2104.08718/) (2021)
- [DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps](https://mlsanity.com/paper/2206.00927/) (2022)
- [Consistency Models](https://mlsanity.com/paper/2303.01469/) (2023)
- [Variational Diffusion Models](https://mlsanity.com/paper/2107.00630/) (2021)
- [StarGAN v2: Diverse Image Synthesis for Multiple Domains](https://mlsanity.com/paper/1912.01865/) (2019)
- [Pick-a-Pic: An Open Dataset of User Preferences for Text-to-Image Generation](https://mlsanity.com/paper/2305.01569/) (2023)
- [Stochastic Interpolants: A Unifying Framework for Flows and Diffusions](https://mlsanity.com/paper/2303.08797/) (2023)
- [DPM-Solver++: Fast Solver for Guided Sampling of Diffusion Probabilistic Models](https://mlsanity.com/paper/2211.01095/) (2022)
- [Fast Sampling of Diffusion Models with Exponential Integrator](https://mlsanity.com/paper/2204.13902/) (2022)
- [3D Shape Generation and Completion through Point-Voxel Diffusion](https://mlsanity.com/paper/2104.03670/) (2021)
- [Consistency Trajectory Models: Learning Probability Flow ODE Trajectory of Diffusion](https://mlsanity.com/paper/2310.02279/) (2023)
- [UniPC: A Unified Predictor-Corrector Framework for Fast Sampling of Diffusion Models](https://mlsanity.com/paper/2302.04867/) (2023)
- [Flow Matching Guide and Code](https://mlsanity.com/paper/2412.06264/) (2024)
- [LayoutDiffusion: Controllable Diffusion Model for Layout-to-image Generation](https://mlsanity.com/paper/2303.17189/) (2023)
- [TRACT: Denoising Diffusion Models with Transitive Closure Time-Distillation](https://mlsanity.com/paper/2303.04248/) (2023)
- [Inductive Moment Matching](https://mlsanity.com/paper/2503.07565/) (2025)
- [Alleviating Exposure Bias in Diffusion Models through Sampling with Shifted Time Steps](https://mlsanity.com/paper/2305.15583/) (2023)
- [Training-free Linear Image Inverses via Flows](https://mlsanity.com/paper/2310.04432/) (2023)
- [Accelerating Diffusion Sampling with Optimized Time Steps](https://mlsanity.com/paper/2402.17376/) (2024)

## Built on by (most cited first, 7 of 7)

- [Entropy Across the Bridge: Conditional-Marginal Discretization for Flow and Schr"odinger Samplers](https://mlsanity.com/paper/2605.16126/) (2026)
- [A Gaussian Perspective for Distributional Discrepancy in Generative Diffusion Models](https://mlsanity.com/paper/2601.13602/) (2026)
- [Learning to Solve Generative ODEs Beyond the Linear Span](https://mlsanity.com/paper/2606.08672/) (2026)
- [I-SplineFlow: Learning Monotone Spline Stochastic Interpolant Schedulers for Few-Step Generation](https://mlsanity.com/paper/2609.27963/) (2026)
- [FACET: Factorized Asymmetric Conditioning for Efficient Transport in High-Fidelity Fluorescence Microscopy Synthesis](https://mlsanity.com/paper/2610.05353/) (2026)
- [Parametric Trajectory Distillation for Few-Step Video Generation](https://mlsanity.com/paper/2610.11498/) (2026)
- [Tikhonov-Stabilized Bezier Representation Forecasting for Training-free Diffusion Acceleration](https://mlsanity.com/paper/2610.16448/) (2026)

## Abstract (arXiv)

We introduce B'ezierFlow, a lightweight training approach for few-step generation with pretrained diffusion and flow models. B'ezierFlow achieves a 2-3x 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 B'ezier 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 B'ezier control points. Across a range of pretrained diffusion and flow models, B'ezierFlow consistently outperforms prior timestep-learning methods, demonstrating the effectiveness of expanding the search space from discrete timesteps to B'ezier-based trajectory transformations.