# Balanced conic rectified flow arXiv: https://arxiv.org/abs/2510.25229 ยท HTML: https://mlsanity.com/paper/2510.25229/ ## Key facts - Cited by 4 papers in the map (data through 14 Oct 2026). - Placed in Flow matching, time series and science, one of 14 directions in Diffusion models. - Builds on 43 of its 59 references that are in the map. - First posted on arXiv 29 Oct 2025. ## Placed in - Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/) ## Builds on (most cited first, 30 of 43) - [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014) - [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020) - [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) - [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021) - [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) - [Consistency Models](https://mlsanity.com/paper/2303.01469/) (2023) - [LSUN: Construction of a Large-scale Image Dataset using Deep Learning with Humans in the Loop](https://mlsanity.com/paper/1506.03365/) (2015) - [One-step Diffusion with Distribution Matching Distillation](https://mlsanity.com/paper/2311.18828/) (2023) - [Improved Precision and Recall Metric for Assessing Generative Models](https://mlsanity.com/paper/1904.06991/) (2019) - [Improving and generalizing flow-based generative models with minibatch optimal transport](https://mlsanity.com/paper/2302.00482/) (2023) - [Score-based Generative Modeling in Latent Space](https://mlsanity.com/paper/2106.05931/) (2021) - [Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modeling](https://mlsanity.com/paper/2106.01357/) (2021) - [Mean Flows for One-step Generative Modeling](https://mlsanity.com/paper/2505.13447/) (2025) - [Optimal Transport for Domain Adaptation](https://mlsanity.com/paper/1507.00504/) (2015) - [Consistency Trajectory Models: Learning Probability Flow ODE Trajectory of Diffusion](https://mlsanity.com/paper/2310.02279/) (2023) - [Improved Techniques for Training Consistency Models](https://mlsanity.com/paper/2310.14189/) (2023) - [InstaFlow: One Step is Enough for High-Quality Diffusion-Based Text-to-Image Generation](https://mlsanity.com/paper/2309.06380/) (2023) - [Knowledge Distillation in Iterative Generative Models for Improved Sampling Speed](https://mlsanity.com/paper/2101.02388/) (2021) - [Simplifying, Stabilizing and Scaling Continuous-Time Consistency Models](https://mlsanity.com/paper/2410.11081/) (2024) - [Diff-Instruct: A Universal Approach for Transferring Knowledge From Pre-trained Diffusion Models](https://mlsanity.com/paper/2305.18455/) (2023) - [Improved Analysis of Score-based Generative Modeling: User-Friendly Bounds under Minimal Smoothness Assumptions](https://mlsanity.com/paper/2211.01916/) (2022) - [Score identity Distillation: Exponentially Fast Distillation of Pretrained Diffusion Models for One-Step Generation](https://mlsanity.com/paper/2404.04057/) (2024) - [On instabilities of deep learning in image reconstruction - Does AI come at a cost?](https://mlsanity.com/paper/1902.05300/) (2019) - [Fast Sampling of Diffusion Models via Operator Learning](https://mlsanity.com/paper/2211.13449/) (2022) - [Solving Schr"odinger Bridges via Maximum Likelihood](https://mlsanity.com/paper/2106.02081/) (2021) - [Inductive Moment Matching](https://mlsanity.com/paper/2503.07565/) (2025) - [Improving the Training of Rectified Flows](https://mlsanity.com/paper/2405.20320/) (2024) ## Built on by (most cited first, 4 of 4) - [Low-Dimensional Adaptation of Rectified Flow: A Diffusion and Stochastic Localization Perspective](https://mlsanity.com/paper/2601.15500/) (2026) - [Optimal Transport Flow Matching by Design](https://mlsanity.com/paper/2606.04092/) (2026) - [Overcoming the Curvature Bottleneck in MeanFlow](https://mlsanity.com/paper/2511.23342/) (2025) - [Optimal Self-Distillation for Rectified Flow via Linear Probing](https://mlsanity.com/paper/2607.14947/) (2026) ## Abstract (arXiv) Rectified flow is a generative model that learns smooth transport mappings between two distributions through an ordinary differential equation (ODE). Unlike diffusion-based generative models, which require costly numerical integration of a generative ODE to sample images with state-of-the-art quality, rectified flow uses an iterative process called reflow to learn smooth and straight ODE paths. This allows for relatively simple and efficient generation of high-quality images. However, rectified flow still faces several challenges. 1) The reflow process requires a large number of generative pairs to preserve the target distribution, leading to significant computational costs. 2) Since the model is typically trained using only generated image pairs, its performance heavily depends on the 1-rectified flow model, causing it to become biased towards the generated data. In this work, we experimentally expose the limitations of the original rectified flow and propose a novel approach that incorporates real images into the training process. By preserving the ODE paths for real images, our method effectively reduces reliance on large amounts of generated data. Instead, we demonstrate that the reflow process can be conducted efficiently using a much smaller set of generated and real images. In CIFAR-10, we achieved significantly better FID scores, not only in one-step generation but also in full-step simulations, while using only of the generative pairs compared to the original method. Furthermore, our approach induces straighter paths and avoids saturation on generated images during reflow, leading to more robust ODE learning while preserving the distribution of real images.