# FACM: Flow-Anchored Consistency Models

arXiv: https://arxiv.org/abs/2507.03738 · HTML: https://mlsanity.com/paper/2507.03738/

## Key facts

- Cited by 16 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 26 of its 33 references that are in the map.
- First posted on arXiv 4 Jul 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, 26 of 26)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [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)
- [Wan: Open and Advanced Large-Scale Video Generative Models](https://mlsanity.com/paper/2503.20314/) (2025)
- [FlashAttention-2: Faster Attention with Better Parallelism and Work Partitioning](https://mlsanity.com/paper/2307.08691/) (2023)
- [Consistency Models](https://mlsanity.com/paper/2303.01469/) (2023)
- [Building Normalizing Flows with Stochastic Interpolants](https://mlsanity.com/paper/2209.15571/) (2022)
- [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)
- [Latent Consistency Models: Synthesizing High-Resolution Images with Few-Step Inference](https://mlsanity.com/paper/2310.04378/) (2023)
- [SiT: Exploring Flow and Diffusion-based Generative Models with Scalable Interpolant Transformers](https://mlsanity.com/paper/2401.08740/) (2024)
- [Representation Alignment for Generation: Training Diffusion Transformers Is Easier Than You Think](https://mlsanity.com/paper/2410.06940/) (2024)
- [Improved Techniques for Training Consistency Models](https://mlsanity.com/paper/2310.14189/) (2023)
- [Reconstruction vs. Generation: Taming Optimization Dilemma in Latent Diffusion Models](https://mlsanity.com/paper/2501.01423/) (2025)
- [One Step Diffusion via Shortcut Models](https://mlsanity.com/paper/2410.12557/) (2024)
- [Understanding Diffusion Objectives as the ELBO with Simple Data Augmentation](https://mlsanity.com/paper/2303.00848/) (2023)
- [Simplifying, Stabilizing and Scaling Continuous-Time Consistency Models](https://mlsanity.com/paper/2410.11081/) (2024)
- [Consistency Models Made Easy](https://mlsanity.com/paper/2406.14548/) (2024)
- [TRACT: Denoising Diffusion Models with Transitive Closure Time-Distillation](https://mlsanity.com/paper/2303.04248/) (2023)
- [Flow map matching with stochastic interpolants: A mathematical framework for consistency models](https://mlsanity.com/paper/2406.07507/) (2024)
- [Align Your Flow: Scaling Continuous-Time Flow Map Distillation](https://mlsanity.com/paper/2506.14603/) (2025)
- [Unified Continuous Generative Models](https://mlsanity.com/paper/2505.07447/) (2025)

## Built on by (most cited first, 16 of 16)

- [Improved Mean Flows: On the Challenges of Fastforward Generative Models](https://mlsanity.com/paper/2512.02012/) (2025)
- [AlphaFlow: Understanding and Improving MeanFlow Models](https://mlsanity.com/paper/2510.20771/) (2025)
- [Transition Models: Rethinking the Generative Learning Objective](https://mlsanity.com/paper/2509.04394/) (2025)
- [SplitMeanFlow: Interval Splitting Consistency in Few-Step Generative Modeling](https://mlsanity.com/paper/2507.16884/) (2025)
- [Decoupled MeanFlow: Turning Flow Models into Flow Maps for Accelerated Sampling](https://mlsanity.com/paper/2510.24474/) (2025)
- [Flow Map Distillation Without Data](https://mlsanity.com/paper/2511.19428/) (2025)
- [SoFlow: Solution Flow Models for One-Step Generative Modeling](https://mlsanity.com/paper/2512.15657/) (2025)
- [Bidirectional Normalizing Flow: From Data to Noise and Back](https://mlsanity.com/paper/2512.10953/) (2025)
- [Universal Inverse Distillation for Matching Models with Real-Data Supervision (No GANs)](https://mlsanity.com/paper/2509.22459/) (2025)
- [CaTok: Taming Mean Flows for One-Dimensional Causal Image Tokenization](https://mlsanity.com/paper/2603.06449/) (2026)
- [From Structure to Detail: Hierarchical Distillation for Efficient Diffusion Model](https://mlsanity.com/paper/2511.08930/) (2025)
- [MFSR: MeanFlow Distillation for One Step Real-World Image Super Resolution](https://mlsanity.com/paper/2603.20690/) (2026)
- [WFR-MFM: One-Step Inference for Dynamic Unbalanced Optimal Transport](https://mlsanity.com/paper/2601.20606/) (2026)
- [FlowConsist: Make Your Flow Consistent with Real Trajectory](https://mlsanity.com/paper/2602.06346/) (2026)
- [Dual-End Consistency Model](https://mlsanity.com/paper/2602.10764/) (2026)
- [A Latent Distribution Perspective on Evaluating and Improving Latent Generative Models](https://mlsanity.com/paper/2609.24088/) (2026)

## Abstract (arXiv)

Continuous-time Consistency Models (CMs) promise efficient few-step generation but face significant challenges with training instability. We argue this instability stems from a fundamental conflict: Training the network exclusively on a shortcut objective leads to the catastrophic forgetting of the instantaneous velocity field that defines the flow. Our solution is to explicitly anchor the model in the underlying flow, ensuring high trajectory fidelity during training. We introduce the Flow-Anchored Consistency Model (FACM), where a Flow Matching (FM) task serves as a dynamic anchor for the primary CM shortcut objective. Key to this Flow-Anchoring approach is a novel expanded time interval strategy that unifies optimization for a single model while decoupling the two tasks to ensure stable, architecturally-agnostic training. By distilling a pre-trained LightningDiT model, our method achieves a state-of-the-art FID of 1.32 with two steps (NFE=2) and 1.70 with just one step (NFE=1) on ImageNet 256x256. To address the challenge of scalability, we develop a memory-efficient Chain-JVP that resolves key incompatibilities with FSDP. This method allows us to scale FACM training on a 14B parameter model (Wan 2.2), accelerating its Text-to-Image inference from 2x40 to 2-8 steps. Our code and pretrained models: https://github.com/ali-vilab/FACM.