# SCoT: Unifying Consistency Models and Rectified Flows via Straight-Consistent Trajectories

arXiv: https://arxiv.org/abs/2502.16972 · HTML: https://mlsanity.com/paper/2502.16972/

## Key facts

- Cited by 7 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 41 of its 46 references that are in the map.
- First posted on arXiv 24 Feb 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 41)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [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)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Rethinking the Inception Architecture for Computer Vision](https://mlsanity.com/paper/1512.00567/) (2015)
- [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)
- [DreamFusion: Text-to-3D using 2D Diffusion](https://mlsanity.com/paper/2209.14988/) (2022)
- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016)
- [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)
- [ProlificDreamer: High-Fidelity and Diverse Text-to-3D Generation with Variational Score Distillation](https://mlsanity.com/paper/2305.16213/) (2023)
- [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)
- [Stochastic Interpolants: A Unifying Framework for Flows and Diffusions](https://mlsanity.com/paper/2303.08797/) (2023)
- [Adversarial Diffusion Distillation](https://mlsanity.com/paper/2311.17042/) (2023)
- [Improved Distribution Matching Distillation for Fast Image Synthesis](https://mlsanity.com/paper/2405.14867/) (2024)
- [Fast Sampling of Diffusion Models with Exponential Integrator](https://mlsanity.com/paper/2204.13902/) (2022)
- [Consistency Trajectory Models: Learning Probability Flow ODE Trajectory of Diffusion](https://mlsanity.com/paper/2310.02279/) (2023)
- [Assessing Generative Models via Precision and Recall](https://mlsanity.com/paper/1806.00035/) (2018)
- [InstaFlow: One Step is Enough for High-Quality Diffusion-Based Text-to-Image Generation](https://mlsanity.com/paper/2309.06380/) (2023)
- [One Step Diffusion via Shortcut Models](https://mlsanity.com/paper/2410.12557/) (2024)
- [Simplifying, Stabilizing and Scaling Continuous-Time Consistency Models](https://mlsanity.com/paper/2410.11081/) (2024)
- [Fast High-Resolution Image Synthesis with Latent Adversarial Diffusion Distillation](https://mlsanity.com/paper/2403.12015/) (2024)
- [Diff-Instruct: A Universal Approach for Transferring Knowledge From Pre-trained Diffusion Models](https://mlsanity.com/paper/2305.18455/) (2023)
- [Score identity Distillation: Exponentially Fast Distillation of Pretrained Diffusion Models for One-Step Generation](https://mlsanity.com/paper/2404.04057/) (2024)

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

- [Distilling Drifting Transformers with Representation Autoencoders](https://mlsanity.com/paper/2606.15553/) (2026)
- [AssetGen: Deployable 3D Asset Generation at Interactive Speed](https://mlsanity.com/paper/2605.26137/) (2026)
- [Reliable AI Needs to Externalize Implicit Knowledge: A Human-AI Collaboration Perspective](https://mlsanity.com/paper/2605.02010/) (2026)
- [DUET: Unified Dual-Space Emotion Control for Diffusion and Flow-Matching Driven Text-to-Speech](https://mlsanity.com/paper/2606.00066/) (2026)
- [ReFPO: Reflow Regularization for Flow Matching Policy Gradients](https://mlsanity.com/paper/2606.21086/) (2026)
- [FreKoo++: Learning Continuous Spectral Dynamics for Temporal Domain Generalization](https://mlsanity.com/paper/2608.22224/) (2026)
- [Iterating Consistency Models: Stability, Error Bounds and Noise Schedules](https://mlsanity.com/paper/2610.03414/) (2026)

## Abstract (arXiv)

Pre-trained diffusion models are commonly used to generate clean data (e.g., images) from random noises, effectively forming pairs of noises and corresponding clean images. Distillation on these pre-trained models can be viewed as the process of constructing advanced trajectories within the pair to accelerate sampling. For instance, consistency model distillation develops consistent projection functions to regulate trajectories, although sampling efficiency remains a concern. Rectified flow method enforces straight trajectories to enable faster sampling, yet relies on numerical ODE solvers, which may introduce approximation errors. In this work, we bridge the gap between the consistency model and the rectified flow method by proposing a Straight Consistent Trajectory~(SCoT) model. SCoT enjoys the benefits of both approaches for fast sampling, producing trajectories with consistent and straight properties simultaneously. These dual properties are strategically balanced by targeting two critical objectives: (1) regulating the gradient of SCoT's mapping to a constant, (2) ensuring trajectory consistency. Extensive experimental results demonstrate the effectiveness and efficiency of SCoT.