# Truncated Consistency Models

arXiv: https://arxiv.org/abs/2410.14895 · HTML: https://mlsanity.com/paper/2410.14895/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 39 of its 45 references that are in the map.
- First posted on arXiv 18 Oct 2024.

## Placed in

- Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/)

## Builds on (most cited first, 30 of 39)

- [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)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Hierarchical Text-Conditional Image Generation with CLIP Latents](https://mlsanity.com/paper/2204.06125/) (2022)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (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)
- [Video Diffusion Models](https://mlsanity.com/paper/2204.03458/) (2022)
- [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)
- [One-step Diffusion with Distribution Matching Distillation](https://mlsanity.com/paper/2311.18828/) (2023)
- [eDiff-I: Text-to-Image Diffusion Models with an Ensemble of Expert Denoisers](https://mlsanity.com/paper/2211.01324/) (2022)
- [Latent Consistency Models: Synthesizing High-Resolution Images with Few-Step Inference](https://mlsanity.com/paper/2310.04378/) (2023)
- [Adversarial Diffusion Distillation](https://mlsanity.com/paper/2311.17042/) (2023)
- [On Distillation of Guided Diffusion Models](https://mlsanity.com/paper/2210.03142/) (2022)
- [Pseudo Numerical Methods for Diffusion Models on Manifolds](https://mlsanity.com/paper/2202.09778/) (2022)
- [Improved Distribution Matching Distillation for Fast Image Synthesis](https://mlsanity.com/paper/2405.14867/) (2024)
- [Score-based Generative Modeling in Latent Space](https://mlsanity.com/paper/2106.05931/) (2021)
- [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)
- [Analyzing and Improving the Training Dynamics of Diffusion Models](https://mlsanity.com/paper/2312.02696/) (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)
- [Make-An-Audio: Text-To-Audio Generation with Prompt-Enhanced Diffusion Models](https://mlsanity.com/paper/2301.12661/) (2023)
- [Fast High-Resolution Image Synthesis with Latent Adversarial Diffusion Distillation](https://mlsanity.com/paper/2403.12015/) (2024)
- [SDXL-Lightning: Progressive Adversarial Diffusion Distillation](https://mlsanity.com/paper/2402.13929/) (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)
- [Fast Sampling of Diffusion Models via Operator Learning](https://mlsanity.com/paper/2211.13449/) (2022)

## Built on by (most cited first, 22 of 22)

- [Align Your Flow: Scaling Continuous-Time Flow Map Distillation](https://mlsanity.com/paper/2506.14603/) (2025)
- [Large Scale Diffusion Distillation via Score-Regularized Continuous-Time Consistency](https://mlsanity.com/paper/2510.08431/) (2025)
- [One-step Diffusion Models with f-Divergence Distribution Matching](https://mlsanity.com/paper/2502.15681/) (2025)
- [Transition Matching Distillation for Fast Video Generation](https://mlsanity.com/paper/2601.09881/) (2026)
- [AnyFlow: Any-Step Video Diffusion Model with On-Policy Flow Map Distillation](https://mlsanity.com/paper/2605.13724/) (2026)
- [Dual-Expert Consistency Model for Efficient and High-Quality Video Generation](https://mlsanity.com/paper/2506.03123/) (2025)
- [CMT: Mid-Training for Efficient Learning of Consistency, Mean Flow, and Flow Map Models](https://mlsanity.com/paper/2509.24526/) (2025)
- [VCT: Training Consistency Models with Variational Noise Coupling](https://mlsanity.com/paper/2502.18197/) (2025)
- [Flow Matching Meets Biology and Life Science: A Survey](https://mlsanity.com/paper/2507.17731/) (2025)
- [Flow Map Distillation Without Data](https://mlsanity.com/paper/2511.19428/) (2025)
- [S4S: Solving for a Diffusion Model Solver](https://mlsanity.com/paper/2502.17423/) (2025)
- [Adaptive Video Distillation: Mitigating Oversaturation and Temporal Collapse in Few-Step Generation](https://mlsanity.com/paper/2603.21864/) (2026)
- [Midpoint Generative Models](https://mlsanity.com/paper/2605.29920/) (2026)
- [CoVAE: Consistency Training of Variational Autoencoders](https://mlsanity.com/paper/2507.09103/) (2025)
- [Cross-Space Distillation: Teaching One-Step Students with Modern Diffusion Teachers](https://mlsanity.com/paper/2606.32020/) (2026)
- [Adaptive Discretization for Consistency Models](https://mlsanity.com/paper/2510.17266/) (2025)
- [Align Your Tangent: Training Better Consistency Models via Manifold-Aligned Tangents](https://mlsanity.com/paper/2510.00658/) (2025)
- [Overcoming the Curvature Bottleneck in MeanFlow](https://mlsanity.com/paper/2511.23342/) (2025)
- [LPM: Industrial-Scale Generative Video Restoration](https://mlsanity.com/paper/2607.13460/) (2026)
- [ChebBooster: A Training-Free Approach for Efficient Diffusion Transformer Inference via Chebyshev-Inspired Extrapolation](https://mlsanity.com/paper/2608.23429/) (2026)
- [Memory-Efficient Training-Free Acceleration of Diffusion Transformers with BaryCache](https://mlsanity.com/paper/2608.28670/) (2026)
- [Consistent Distribution Matching for Data-Free Diffusion Distillation](https://mlsanity.com/paper/2610.09221/) (2026)

## Abstract (arXiv)

Consistency models have recently been introduced to accelerate sampling from diffusion models by directly predicting the solution (i.e., data) of the probability flow ODE (PF ODE) from initial noise. However, the training of consistency models requires learning to map all intermediate points along PF ODE trajectories to their corresponding endpoints. This task is much more challenging than the ultimate objective of one-step generation, which only concerns the PF ODE's noise-to-data mapping. We empirically find that this training paradigm limits the one-step generation performance of consistency models. To address this issue, we generalize consistency training to the truncated time range, which allows the model to ignore denoising tasks at earlier time steps and focus its capacity on generation. We propose a new parameterization of the consistency function and a two-stage training procedure that prevents the truncated-time training from collapsing to a trivial solution. Experiments on CIFAR-10 and ImageNet 64×64 datasets show that our method achieves better one-step and two-step FIDs than the state-of-the-art consistency models such as iCT-deep, using more than 2× smaller networks. Project page: https://truncated-cm.github.io/