Awesome-Consistency-Models

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<div align="center">
  <img src="logo.png" alt="logo" width="400" />
  <br>
  <strong>Awesome list of consistency models</strong>
</div>

Consistency models represent a class of generative models that enable high-quality sample generation in one or few steps, addressing the iterative sampling limitations of traditional diffusion models. Introduced in the seminal work "Consistency Models" (ICML 2023), they achieve this by learning a mapping from noise to data that satisfies a self-consistency property, allowing direct distillation from pretrained diffusion models or training from scratch. This approach has led to state-of-the-art results in few-step generation, with applications spanning image synthesis, audio, video, and beyond. Subsequent advancements have focused on stability, scalability, and extensions to new domains like robotics and 3D generation.

Papers are sorted by publication year in descending order, focusing on key contributions in consistency models and related advancements.

## 2025
- **Inductive Moment Matching**  
  [arXiv:2503.07565](https://arxiv.org/abs/2503.07565)  
  Proposes Inductive Moment Matching (IMM), a new class of generative models for one- or few-step sampling with a single-stage training procedure, resolving trade-offs in diffusion and flow matching models.
- **MotionPCM: Real-Time Motion Synthesis with Phased Consistency Model**  
  [arXiv:2501.19083](https://arxiv.org/abs/2501.19083)  
  Introduces MotionPCM, a phased consistency model-based approach for real-time text-conditioned human motion synthesis in latent space, achieving over 30 FPS in single-step inference.
- **Mean Flows for One-step Generative Modeling**  
  [arXiv:2505.13447](https://arxiv.org/abs/2505.13447)  
  Introduces average velocity to characterize flow fields for one-step generation, deriving an identity between average and instantaneous velocities to guide training; achieves FID 3.43 on ImageNet 256x256 from scratch.
- **AlphaFlow: Understanding and Improving MeanFlow Models**  
  [arXiv:2510.20771](https://arxiv.org/abs/2510.20771)  
  Decomposes the MeanFlow objective into trajectory flow matching and consistency, proposing AlphaFlow to improve one-step generation; achieves new SOTA FID scores with vanilla DiT backbones.
- **Decoupled MeanFlow: Turning Flow Models into Flow Maps for Accelerated Sampling**  
  [arXiv:2510.24474](https://arxiv.org/abs/2510.24474)  
  Introduces Decoupled MeanFlow (DMF), converting pretrained flow models into flow maps without architectural changes; enables high-quality 1-step generation via fine-tuning.
- **MP1: MeanFlow Tames Policy Learning in 1-step for Robotic Manipulation**  
  [arXiv:2507.10543](https://arxiv.org/abs/2507.10543)  
  Adapts MeanFlow for robotic manipulation, enabling one-step action generation from 3D point clouds; outperforms DP3 by 10.2% success rate with 19x faster inference.
- **MeanFlowSE: One-Step Generative Speech Enhancement via MeanFlow**  
  [arXiv:2509.23299](https://arxiv.org/abs/2509.23299)  
  Integrates MeanFlow with SSL conditioning for one-step speech enhancement; achieves SOTA perceptual quality with low RTF on DNS Challenge datasets.
- **MeanFlowSE: one-step generative speech enhancement via conditional mean flow**  
  [arXiv:2509.14858](https://arxiv.org/abs/2509.14858)  
  Learns average-velocity fields for conditional speech enhancement; single-step model attains highest quality on VoiceBank-DEMAND with low computational cost.

## 2024 and Earlier
- **Real-time One-Step Diffusion-based Expressive Portrait Videos Generation**  
  [arXiv:2412.13479](https://arxiv.org/abs/2412.13479)  
  Introduces OSA-LCM for one-step expressive portrait video generation from a single image and audio; outperforms open-source models in efficiency and quality.
- **From Slow Bidirectional to Fast Causal Video Generators**  
  [arXiv:2412.07772](https://arxiv.org/abs/2412.07772)  
  Distills bidirectional diffusion models into few-step causal generators using asymmetric distillation; enables 9.4 FPS streaming on a single GPU.
- **DOLLAR: Few-Step Video Generation via Distillation and Latent Reward Optimization**  
  [arXiv:2412.15689](https://arxiv.org/abs/2412.15689)  
  Combines one-step distillation and latent reward optimization for few-step video generation; accelerates teacher models by 278.6x with superior 4-step quality.
- **SnapGen-V: Generating a Five-Second Video within Five Seconds on a Mobile Device**  
  [arXiv:2412.10494](https://arxiv.org/abs/2412.10494)  
  A 0.6B parameter model for mobile video generation; produces 5-second videos in 5 seconds on iPhone 16 using adversarial fine-tuning and 4-step denoising.
- **Consistency Diffusion Bridge Models**  
  [arXiv:2410.22637](https://arxiv.org/abs/2410.22637)  
  Extends consistency models to diffusion denoising bridge models for image-to-image tasks; enables 50x faster sampling with improved quality.
- **One Step Diffusion via Shortcut Models**  
  [arXiv:2410.12557](https://arxiv.org/abs/2410.12557)  
  Introduces shortcut models for one- or few-step generation using step-size conditioning; single network outperforms distillation methods across budgets.
- **Stable Consistency Tuning: Understanding and Improving Consistency Models**  
  [arXiv:2410.18958](https://arxiv.org/abs/2410.18958)  
  Frames consistency training as TD learning in an MDP; proposes SCT with variance-reduced targets, achieving new SOTA FID 1.55 (2-step) on ImageNet-64.
- **Simplifying, Stabilizing and Scaling Continuous-Time Consistency Models**  
  [arXiv:2410.11081](https://arxiv.org/abs/2410.11081)  
  Stabilizes continuous-time CM training with two-step sampling; achieves FID 1.88 on ImageNet 512x512, closing the gap with diffusion models to 10%.
- **Presto! Distilling Steps and Layers for Accelerating Music Generation**  
  [arXiv:2410.05167](https://arxiv.org/abs/2410.05167)  
  Combines score-based DMD and layer distillation for TTM; accelerates by 10-18x with RTF 0.013, fastest TTM model.
- **Target-Driven Distillation: Consistency Distillation with Target Timestep Selection and Decoupled Guidance**  
  [arXiv:2409.01347](https://arxiv.org/abs/2409.01347)  
  Improves consistency distillation with refined timestep selection and decoupled guidance; SOTA in few-step generation with flexible inference.
- **Consistency Models Made Easy**  
  [arXiv:2406.14548](https://arxiv.org/abs/2406.14548)  
  Proposes Easy Consistency Tuning (ECT) for efficient CM training from pretrained diffusion models; 2-step FID 2.73 on CIFAR-10 in 1 hour on A100.
- **Motion Consistency Model: Accelerating Video Diffusion with Disentangled Motion-Appearance Distillation**  
  [arXiv:2406.06890](https://arxiv.org/abs/2406.06890)  
  Disentangles motion and appearance for video distillation; enables few-step generation with high frame quality using image data enhancement.
- **ManiCM: Real-time 3D Diffusion Policy via Consistency Model for Robotic Manipulation**  
  [arXiv:2406.01586](https://arxiv.org/abs/2406.01586)  
  Applies consistency models to 3D diffusion policies for one-step robotic actions; 10x faster than SOTA with competitive success rates.
- **Phased Consistency Models**  
  [arXiv:2405.18407](https://arxiv.org/abs/2405.18407)  
  Generalizes latent consistency models by addressing key flaws; outperforms LCMs in 1-16 step text-conditioned image generation.
- **Consistency Policy: Accelerated Visuomotor Policies via Consistency Distillation**  
  [arXiv:2405.07503](https://arxiv.org/abs/2405.07503)  
  Distills diffusion policies into consistency policies for low-latency visuomotor control; 10x faster inference on resource-constrained robots.
- **Multistep Consistency Models**  
  [arXiv:2403.06807](https://arxiv.org/abs/2403.06807)  
  Unifies consistency and diffusion models for trade-off between speed and quality; enables easy training for 2-8 step generation.
- **Generalized Consistency Trajectory Models for Image Manipulation**  
  [arXiv:2403.12510](https://arxiv.org/abs/2403.12510)  
  Extends CTMs to arbitrary distribution translation via ODEs; enables one-step image editing and restoration.
- **SCott: Accelerating Diffusion Models with Stochastic Consistency Distillation**  
  [arXiv:2403.01505](https://arxiv.org/abs/2403.01505)  
  Integrates SDE solvers into consistency distillation for text-to-image; 2-step FID 22.1 on MS-COCO, surpassing prior SOTA.
- **Bidirectional Consistency Models**  
  [arXiv:2403.18035](https://arxiv.org/abs/2403.18035)  
  Learns bidirectional traversal of PF ODE for unified generation and inversion; enables one-step tasks with additional refinement steps.
- **CCM: Adding Conditional Controls to Text-to-Image Consistency Models**  
  [arXiv:2312.06971](https://arxiv.org/abs/2312.06971)  
  Explores strategies for adding ControlNet-like controls to CMs; supports edge, depth, pose, and masked image conditioning.
- **ACT-Diffusion: Efficient Adversarial Consistency Training for One-step Diffusion Models**  
  [arXiv:2311.14097](https://arxiv.org/abs/2311.14097)  
  Uses adversarial training to minimize JS divergence in consistency models; halves parameters and steps with improved quality.
- **Consistency Trajectory Models: Learning Probability Flow ODE Trajectory of Diffusion**  
  [arXiv:2310.02279](https://arxiv.org/abs/2310.02279)  
  Generalizes CMs to learn arbitrary PF ODE traversals; enables long-jump sampling with SOTA single-step FID.
- **Improved Techniques for Training Consistency Models**  
  [arXiv:2310.14189](https://arxiv.org/abs/2310.14189)  
  Enables direct consistency training from data without distillation; achieves single-step FID 2.51 on CIFAR-10.
- **Latent Consistency Models: Synthesizing High-Resolution Images with Few-Step Inference**  
  [arXiv:2310.04378](https://arxiv.org/abs/2310.04378)  
  Distills LDMs into latent consistency models; enables 2-4 step 768x768 generation in 32 A100 hours.
- **Music Consistency Models**  
  [arXiv:2404.13358](https://arxiv.org/abs/2404.13358)  
  Applies consistency distillation to text-to-music diffusion; enables few-step mel-spectrogram synthesis with adversarial training.
- **RL for Consistency Models: Faster Reward Guided Text-to-Image Generation**  
  [arXiv:2404.03673](https://arxiv.org/abs/2404.03673)  
  Frames CM inference as RL for reward optimization; enables fast adaptation to objectives like aesthetics.
- **Towards a mathematical theory for consistency training in diffusion models**  
  [arXiv:2402.07802](https://arxiv.org/abs/2402.07802)  
  Provides convergence guarantees for consistency training under score-matching and smoothness assumptions.
- **Convergence guarantee for consistency models**  
  [arXiv:2308.11449](https://arxiv.org/abs/2308.11449)  
  Establishes W2 convergence for one-step CM sampling under L2-accurate assumptions.
- **CoMoSpeech: One-Step Speech and Singing Voice Synthesis via Consistency Model**  
  [arXiv:2305.06908](https://arxiv.org/abs/2305.06908)  
  Distills diffusion TTS into one-step consistency models; 150x faster than real-time on A100.
- **Consistency Models**  
  [arXiv:2303.01469](https://arxiv.org/abs/2303.01469)  
  Introduces consistency models for one-step generation; SOTA FID 3.55 on CIFAR-10.

## Further Reading
- **Score-Based Generative Modeling through Stochastic Differential Equations**  
  [arXiv:2011.13456](https://arxiv.org/abs/2011.13456) (ICLR 2021)  
  Foundational work on score-based generative models via SDEs.
- **Flow Matching for Generative Modeling**  
  [arXiv:2210.02747](https://arxiv.org/abs/2210.02747) (ICLR 2023)  
  Introduces flow matching as a simulation-free alternative to diffusion.
- **Elucidating the Design Space of Diffusion-Based Generative Models**  
  [arXiv:2206.00364](https://arxiv.org/abs/2206.00364) (NeurIPS 2022)  
  Surveys the design space of diffusion models.
- **Denoising Diffusion Probabilistic Models**  
  [arXiv:2006.11239](https://arxiv.org/abs/2006.11239) (NeurIPS 2020)  
  Seminal paper on DDPMs for image generation.
- **Stable Target Field for Reduced Variance Score Estimation in Diffusion Models**  
  [arXiv:2302.00670](https://arxiv.org/abs/2302.00670) (ICLR 2023)  
  Improves score estimation variance in diffusion models.
- **Denoising Diffusion Implicit Models**  
  [arXiv:2010.02502](https://arxiv.org/abs/2010.02502) (ICLR 2021)  
  Introduces DDIMs for faster sampling.
- **DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps**  
  [arXiv:2206.00927](https://arxiv.org/abs/2206.00927) (NeurIPS 2022)  
  Efficient ODE solver reducing steps to ~10.
- **Progressive Distillation for Fast Sampling of Diffusion Models**  
  [arXiv:2202.00512](https://arxiv.org/abs/2202.00512) (ICLR 2022)  
  Distills diffusion models progressively for fewer steps.
- **On Distillation of Guided Diffusion Models**  
  [arXiv:2306.00927](https://arxiv.org/abs/2306.00927) (CVPR 2023)  
  Distills guided diffusion models.
- **Score identity Distillation: Exponentially Fast Distillation of Pretrained Diffusion Models for One-Step Generation**  
  [arXiv:2404.04057](https://arxiv.org/abs/2404.04057) (ICML 2024)  
  Exponential speedup via score identity distillation.
- **Discrete Flow Matching**  
  [arXiv:2407.15595](https://arxiv.org/abs/2407.15595) (arXiv 2024)  
  Discrete variant of flow matching.
- **Rectified Diffusion: Straightness Is Not Your Need in Rectified Flow**  
  [arXiv:2410.07303](https://arxiv.org/abs/2410.07303) (arXiv 2024)  
  Improves rectified flow without straightness.
- **Fast ODE-based Sampling for Diffusion Models in Around 5 Steps**  
  [arXiv:2312.00094](https://arxiv.org/abs/2312.00094) (ICML 2024)  
  Reduces steps to ~5 with ODE solving.
- **AN OVERLOOKED INGREDIENT FOR RECTIFIED FLOW: REAL SAMPLES**  
  [arXiv:2402.19159](https://arxiv.org/abs/2402.19159) (OpenReview 2024)  
  Emphasizes real samples in rectified flow.
- **SwiftBrush: One-Step Text-to-Image Diffusion Model with Variational Score Distillation**  
  [arXiv:2312.05239](https://arxiv.org/abs/2312.05239) (CVPR 2024)  
  One-step T2I with variational distillation.
- **Inconsistencies In Consistency Models: Better ODE Solving Does Not Imply Better Samples**  
  [arXiv:2411.08954](https://arxiv.org/abs/2411.08954) (NeurIPS 2024 Workshop)  
  Analyzes limitations of consistency models in multi-step sampling.
- **Understanding Hallucinations in Diffusion Models through Mode Interpolation**  
  [arXiv:2406.09358](https://arxiv.org/abs/2406.09358) (arXiv 2024)  
  Explores hallucinations via mode interpolation.
- **Rethinking Score Distillation as a Bridge Between Image Distributions**  
  [arXiv:2406.09417](https://arxiv.org/abs/2406.09417) (arXiv 2024)  
  Reframes score distillation for distributions.
- **One-Step Diffusion Distillation through Score Implicit Matching**  
  [arXiv:2410.16794](https://arxiv.org/abs/2410.16794) (NeurIPS 2024)  
  One-step distillation via score matching.
- **Distilled Decoding 1: One-step Sampling of Image Auto-regressive Models with Flow Matching**  
  [arXiv:2412.17153](https://arxiv.org/abs/2412.17153) (arXiv 2024)  
  One-step sampling for autoregressive models.
- **The Fokker Planck Equation and Diffusion Models**  
  [Blog](https://www.peterholderrieth.com/blog/2023/The-Fokker-Planck-Equation-and-Diffusion-Models/)  
  Explains FP equation in diffusion context.
- **Generative AI and Foundation Models, Spring 2024 by Ernest K. Ryu**  
  [Course Page](https://ernestryu.com/courses/FM.html)  
  Course on generative AI and foundation models.
- **A Visual Dive into Conditional Flow Matching**  
  [Blog](https://dl.heeere.com/conditional-flow-matching/blog/conditional-flow-matching/)  
  Visual explanation of conditional flow matching.
- **Soft Diffusion: Score Matching for General Corruptions**  
  [arXiv:2209.05442](https://arxiv.org/abs/2209.05442) (arXiv 2022)  
  Score matching for general corruptions.
- **Consistent Flow Distillation for Text-to-3D Generation**  
  [arXiv:2501.05445](https://arxiv.org/abs/2501.05445) (arXiv 2025)  
  Flow distillation for T2 3D.
- **Visual Generation Without Guidance**  
  [arXiv:2501.15420](https://arxiv.org/abs/2501.15420) (arXiv 2025)  
  Unguided visual generation.
- **PSEUDO NUMERICAL METHODS FOR DIFFUSION MODELS ON MANIFOLDS**  
  [arXiv:2202.09778](https://arxiv.org/abs/2202.09778) (ICLR 2022)  
  Pseudo methods for manifold diffusion.
- **Efficient, Accurate and Stable Gradients for Neural ODEs**  
  [arXiv:2003.03444](https://arxiv.org/abs/2003.03444) (arXiv 2020)  
  Stable gradients for neural ODEs.
- **BLOCK DIFFUSION: INTERPOLATING BETWEEN AUTOREGRESSIVE AND DIFFUSION LANGUAGE MODELS**  
  [arXiv:2402.03300](https://arxiv.org/abs/2402.03300) (ICLR 2025)  
  Interpolates AR and diffusion LMs.
- **Distilling ODE Solvers of Diffusion Models into Smaller Steps**  
  [arXiv:2309.16421](https://arxiv.org/abs/2309.16421) (CVPR 2024)  
  Distills ODE solvers for fewer steps.
- **Back to Basics: Revisiting REINFORCE Style Optimization for Learning from Human Feedback in LLMs**  
  [arXiv:2402.14740](https://arxiv.org/abs/2402.14740)  
  Revisits REINFORCE for LLM alignment.
- **ReMax: A Simple, Effective, and Efficient Reinforcement Learning Method for Aligning Large Language Models**  
  [arXiv:2310.10505](https://arxiv.org/abs/2310.10505)  
  RL method for LLM alignment.
- **DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models**  
  [arXiv:2402.03300](https://arxiv.org/abs/2402.03300)  
  Advances math reasoning in open LMs.
- **Understanding R1-Zero-Like Training: A Critical Perspective**  
  [arXiv:2503.20783](https://arxiv.org/abs/2503.20783)  
  Critical view on R1-Zero training.

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