Awesome Consistency Models

A curated reading list centered on consistency models: generative models that learn to map points on the same probability-flow ODE trajectory to a common data endpoint, enabling one- or few-step sampling. They can be trained through consistency distillation from a diffusion teacher or consistency training from data. Start with the original Consistency Models paper.

The list also covers related flow-based generators, distribution matching, and score distillation applications. These connections are useful, but the methods optimize different objects and should not all be called consistency models.

Contents

• Scope and method families
• Suggested reading paths
• Core consistency models
• Applications
  • Images, editing, and control
  • Video and human motion
  • Audio, speech, and music
  • Robotics and policies
• Related few-step generation
• Score distillation for SVG and 3D
• Foundations and sampling
• Learning resources
• Contributing

Scope and method families

These are reading categories, not mutually exclusive definitions: hybrid methods can combine several objectives. In particular, SDS / VSD asset optimization is different from consistency distillation. VectorFusion and SVGDreamer optimize vector graphics for a prompt; their inclusion does not imply one-step SVG inference.

Within each paper subsection, entries are ordered by first preprint date, newest first; arXiv identifiers make that date visible. Venue years, when supplied, are separate: VectorFusion first appeared in 2022 and was published at CVPR 2023; SVGDreamer first appeared in 2023 and was published at CVPR 2024. This is a selected bibliography, not an exhaustive survey or a benchmark ranking.

Suggested reading paths

The arrows suggest a reading sequence, rather than claiming every method is a direct extension of the previous one.

Core consistency models

Training and trajectory models

• Stable Consistency Tuning: Understanding and Improving Consistency Models
  arXiv:2410.18958
  Interprets consistency learning as temporal-difference learning and introduces score-identity-based variance reduction for more stable tuning.

• Simplifying, Stabilizing and Scaling Continuous-Time Consistency Models
  arXiv:2410.11081
  Revises parameterization, architecture, and objectives to stabilize continuous-time consistency training at larger model and image scales.

• Consistency Models Made Easy
  arXiv:2406.14548
  Introduces Easy Consistency Tuning (ECT): starts from a pretrained diffusion model and progressively strengthens the consistency condition.

• Bidirectional Consistency Models
  arXiv:2403.18035
  Learns forward and backward traversal of a probability-flow ODE in one network, supporting both generation and inversion.

• Multistep Consistency Models
  arXiv:2403.06807
  Connects diffusion and consistency modeling to support a trade-off between generation quality and sampling cost.

• ACT-Diffusion: Efficient Adversarial Consistency Training for One-step Diffusion Models
  arXiv:2311.14097
  Adds adversarial distribution matching to consistency training to improve one-step generation and reduce training resource requirements.

• Improved Techniques for Training Consistency Models
  arXiv:2310.14189
  Removes the teacher's exponential moving average, adopts a Pseudo-Huber loss, and revises noise and discretization schedules for training directly from data.

• Consistency Trajectory Models: Learning Probability Flow ODE Trajectory of Diffusion
  arXiv:2310.02279
  Learns mappings between arbitrary times on a probability-flow ODE trajectory, extending the endpoint mapping used by consistency models.

• Consistency Models
  arXiv:2303.01469 · Official code (archived)
  Introduces self-consistent mappings from points on a probability-flow ODE trajectory to its data endpoint, trained by distillation or directly from data.

Theory and analysis

• Inconsistencies In Consistency Models: Better ODE Solving Does Not Imply Better Samples
  arXiv:2411.08954 (NeurIPS 2024 Workshop)
  Shows that directly reducing probability-flow ODE approximation error can worsen sample quality, highlighting a limitation of solver-based interpretations.

• Towards a mathematical theory for consistency training in diffusion models
  arXiv:2402.07802
  Studies distributional convergence of consistency training under explicit assumptions on the training process and data distribution.

• Convergence guarantee for consistency models
  arXiv:2308.11449
  Provides Wasserstein convergence guarantees under score error, consistency error, and smoothness assumptions.

Applications

Includes consistency-based applications and explicitly labeled neighboring approaches. Labels describe the main connection to this list.

Images, editing, and control

• Consistency Diffusion Bridge Models
  arXiv:2410.22637
  Extends consistency training and distillation to diffusion bridges for fast translation between paired data distributions.

• Target-Driven Distillation: Consistency Distillation with Target Timestep Selection and Decoupled Guidance
  arXiv:2409.01347
  Refines target timestep selection and decouples guidance during consistency distillation, allowing guidance adjustment at inference.

• Phased Consistency Models
  arXiv:2405.18407
  Generalizes latent consistency modeling with a phased design for multi-step refinement in image and video generation.

• RL for Consistency Models: Faster Reward Guided Text-to-Image Generation
  arXiv:2404.03673
  Uses reinforcement learning to adapt consistency models to reward objectives for text-to-image generation.

• Generalized Consistency Trajectory Models for Image Manipulation
  arXiv:2403.12510
  Generalizes consistency trajectory models to ODE transport between arbitrary distributions for translation, restoration, and editing.

• SCott: Accelerating Diffusion Models with Stochastic Consistency Distillation
  arXiv:2403.01505
  Uses stochastic differential equation solvers within consistency distillation for few-step text-to-image generation.

• Trajectory Consistency Distillation: Improved Latent Consistency Distillation by Semi-Linear Consistency Function with Trajectory Mapping
  arXiv:2402.19159
  Introduces trajectory consistency parameterization and stochastic sampling to improve latent consistency distillation across sampling budgets.

• CCM: Adding Conditional Controls to Text-to-Image Consistency Models
  arXiv:2312.06971
  Adds spatial conditioning, including edges, depth, poses, and masks, to text-to-image consistency models.

• LCM-LoRA: A Universal Stable-Diffusion Acceleration Module
  arXiv:2311.05556 · Official code
  Uses low-rank consistency distillation to obtain acceleration adapters that can be combined with compatible Stable Diffusion fine-tunes and LoRAs.

• Latent Consistency Models: Synthesizing High-Resolution Images with Few-Step Inference
  arXiv:2310.04378 · Official code
  Distills guided latent diffusion models into consistency models for few-step high-resolution text-to-image synthesis.

Video and human motion

• MotionPCM: Real-Time Motion Synthesis with Phased Consistency Model
  arXiv:2501.19083
  Applies phased consistency modeling to text-conditioned human motion synthesis in latent space.

• DOLLAR: Few-Step Video Generation via Distillation and Latent Reward Optimization
  arXiv:2412.15689
  Hybrid: consistency + variational score distillation. Combines few-step video distillation with latent reward optimization.

• Real-time One-Step Diffusion-based Expressive Portrait Videos Generation
  arXiv:2412.13479
  Uses OSA-LCM for one-step expressive portrait video generation conditioned on a reference image and audio.

• SnapGen-V: Generating a Five-Second Video within Five Seconds on a Mobile Device
  arXiv:2412.10494
  Related: adversarial fine-tuning. Combines a compact video generator with few-step denoising for generation on mobile devices.

• From Slow Bidirectional to Fast Autoregressive Video Diffusion Models
  arXiv:2412.07772
  Related: DMD (CausVid). Distills a bidirectional video teacher into a causal student using distribution matching and asymmetric teacher-student attention.

• Motion Consistency Model: Accelerating Video Diffusion with Disentangled Motion-Appearance Distillation
  arXiv:2406.06890
  Separates video motion distillation from image-based appearance learning to improve few-step video synthesis.

Audio, speech, and music

The two MeanFlowSE papers below are independent works by different author teams.

• MeanFlowSE: One-Step Generative Speech Enhancement via MeanFlow
  arXiv:2509.23299
  Related: MeanFlow; Zhu et al. Uses self-supervised speech representations to condition one-step latent speech enhancement.

• MeanFlowSE: one-step generative speech enhancement via conditional mean flow
  arXiv:2509.14858
  Related: MeanFlow; Li et al. Learns conditional average-velocity fields for speech enhancement without a teacher; evaluated on VoiceBank-DEMAND.

• Presto! Distilling Steps and Layers for Accelerating Music Generation
  arXiv:2410.05167
  Related: DMD. Combines distribution matching across sampling steps with layer distillation to reduce music generation cost.

• Music Consistency Models
  arXiv:2404.13358
  Combines consistency distillation and adversarial training for few-step text-conditioned music mel-spectrogram generation.

• CoMoSpeech: One-Step Speech and Singing Voice Synthesis via Consistency Model
  arXiv:2305.06908
  Distills a diffusion teacher into a one-step consistency model for speech and singing voice synthesis.

Robotics and policies

• MP1: MeanFlow Tames Policy Learning in 1-step for Robotic Manipulation
  arXiv:2507.10543
  Related: MeanFlow. Learns one-step robot action generation conditioned on 3D point clouds.

• ManiCM: Real-time 3D Diffusion Policy via Consistency Model for Robotic Manipulation
  arXiv:2406.01586
  Distills a 3D diffusion policy into a consistency model for low-latency robotic manipulation.

• Consistency Policy: Accelerated Visuomotor Policies via Consistency Distillation
  arXiv:2405.07503
  Applies consistency distillation to diffusion policies for faster visuomotor control.

Related few-step generation

Flow maps and distribution-level training

• Decoupled MeanFlow: Turning Flow Models into Flow Maps for Accelerated Sampling
  arXiv:2510.24474
  Converts pretrained flow models into flow maps for accelerated sampling through fine-tuning.

• AlphaFlow: Understanding and Improving MeanFlow Models
  arXiv:2510.20771
  Analyzes the MeanFlow objective through trajectory flow matching and consistency, and uses the decomposition to improve training.

• Mean Flows for One-step Generative Modeling
  arXiv:2505.13447
  Learns average velocity over a time interval through an identity relating it to instantaneous velocity, enabling one-step generation from scratch.

• Inductive Moment Matching
  arXiv:2503.07565
  Uses inductive distribution matching to train a one- or few-step generator in a single stage, without a pretrained teacher.

• One Step Diffusion via Shortcut Models
  arXiv:2410.12557
  Conditions a single network on noise level and desired step size, supporting different sampling budgets after one training stage.

• Rectified Diffusion: Straightness Is Not Your Need in Rectified Flow
  arXiv:2410.07303 (arXiv 2024)
  Revisits the role of straight trajectories in rectification and extends the approach to diffusion models.

• An Overlooked Ingredient for Rectified Flow: Real Samples
  OpenReview PDF (2024 submission)
  Studies incorporating real samples into rectified flow training instead of relying only on generated reflow pairs.

Generator distillation

• Distilled Decoding 1: One-step Sampling of Image Auto-regressive Models with Flow Matching
  arXiv:2412.17153 (arXiv 2024)
  Uses flow matching to distill an image autoregressive model into a one-step generator.

• One-Step Diffusion Distillation through Score Implicit Matching
  arXiv:2410.16794 (NeurIPS 2024)
  Introduces score implicit matching for distilling diffusion models into one-step generators.

• Improved Distribution Matching Distillation for Fast Image Synthesis
  arXiv:2405.14867 (NeurIPS 2024) · Project · Official code
  DMD2 removes paired regression data, stabilizes critic updates, and combines adversarial training with a procedure for few-step generation.

• Score identity Distillation: Exponentially Fast Distillation of Pretrained Diffusion Models for One-Step Generation
  arXiv:2404.04057 (ICML 2024)
  Uses score identities to distill a pretrained diffusion model into a one-step generator.

• SwiftBrush: One-Step Text-to-Image Diffusion Model with Variational Score Distillation
  arXiv:2312.05239 (CVPR 2024)
  Adapts variational score distillation to train a one-step text-to-image student without a training image dataset.

• One-step Diffusion with Distribution Matching Distillation
  arXiv:2311.18828 (CVPR 2024)
  Trains a one-step generator using a distribution-matching gradient derived from teacher and generated-data scores, together with a regression loss.

• Distilling ODE Solvers of Diffusion Models into Smaller Steps
  arXiv:2309.16421 (CVPR 2024)
  Distills ODE solvers for fewer steps.

• On Distillation of Guided Diffusion Models
  arXiv:2210.03142
  Distills classifier-free guidance into a single network and then progressively reduces the number of denoising steps.

• Progressive Distillation for Fast Sampling of Diffusion Models
  arXiv:2202.00512 (ICLR 2022)
  Repeatedly distills two teacher sampling steps into one student step to reduce the sampling budget.

Score distillation for SVG and 3D

These methods transfer an image generative prior to an asset representation through optimization. Read this section alongside generator distillation to compare per-asset optimization with training a reusable generator.

SVG generation

• SVGDreamer: Text Guided SVG Generation with Diffusion Model
  arXiv:2312.16476 (CVPR 2024) · Project · Official code
  Combines Semantic-driven Image Vectorization (SIVE) for editable foreground/background elements with Vectorized Particle-based Score Distillation (VPSD) for SVG quality and diversity.

• VectorFusion: Text-to-SVG by Abstracting Pixel-Based Diffusion Models
  arXiv:2211.11319 (CVPR 2023) · CVPR paper · Project
  Optimizes SVG paths through a differentiable rasterizer using Score Distillation Sampling (SDS) from a pretrained text-to-image diffusion model; supports random or vectorized-image initialization.

3D and score distillation foundations

• Consistent Flow Distillation for Text-to-3D Generation
  arXiv:2501.05445 (arXiv 2025)
  Uses sampling-flow gradients and multi-view consistent Gaussian noise to guide text-to-3D optimization with an image diffusion prior.

• Rethinking Score Distillation as a Bridge Between Image Distributions
  arXiv:2406.09417 (arXiv 2024)
  Interprets score distillation as transport between image distributions to analyze its behavior and improve generation.

• ProlificDreamer: High-Fidelity and Diverse Text-to-3D Generation with Variational Score Distillation
  arXiv:2305.16213 (NeurIPS 2023)
  Introduces Variational Score Distillation (VSD), treating scene parameters as a distribution to address quality and diversity limitations of SDS.

• DreamFusion: Text-to-3D using 2D Diffusion
  arXiv:2209.14988
  Introduces SDS to optimize a 3D representation through rendered views using a frozen text-to-image diffusion prior.

Foundations and sampling

Diffusion and flow modeling

• Visual Generation Without Guidance
  arXiv:2501.15420 (arXiv 2025)
  Studies visual generation without explicit guidance at sampling time.

• Understanding Hallucinations in Diffusion Models through Mode Interpolation
  arXiv:2406.09358 (arXiv 2024)
  Studies how interpolation between data modes can lead diffusion models to generate samples outside the data distribution.

• Stable Target Field for Reduced Variance Score Estimation in Diffusion Models
  arXiv:2302.00670 (ICLR 2023)
  Reduces the variance of score estimation targets during diffusion training.

• Flow Matching for Generative Modeling
  arXiv:2210.02747 (ICLR 2023)
  Learns continuous transport through regression on conditional vector fields, without simulating model trajectories during training.

• Soft Diffusion: Score Matching for General Corruptions
  arXiv:2209.05442 (arXiv 2022)
  Generalizes score-based modeling to corruption processes beyond standard Gaussian noise.

• Elucidating the Design Space of Diffusion-Based Generative Models
  arXiv:2206.00364 (NeurIPS 2022)
  Analyzes and improves diffusion model design choices, including preconditioning, training, and sampling.

• Score-Based Generative Modeling through Stochastic Differential Equations
  arXiv:2011.13456 (ICLR 2021)
  Unifies score-based generation using stochastic differential equations and the associated probability-flow ODE.

• Denoising Diffusion Probabilistic Models
  arXiv:2006.11239 (NeurIPS 2020)
  Develops diffusion-based image generation through learned reversal of a gradual noising process.

Numerical methods and fast samplers

• Efficient, Accurate and Stable Gradients for Neural ODEs
  arXiv:2410.11648
  Introduces algebraically reversible ODE solvers for accurate gradients with reduced memory and recomputation costs.

• Fast ODE-based Sampling for Diffusion Models in Around 5 Steps
  arXiv:2312.00094 (ICML 2024)
  Develops efficient ODE-based sampling for diffusion models at small evaluation budgets.

• DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps
  arXiv:2206.00927 (NeurIPS 2022)
  Develops a high-order solver specialized for diffusion probability-flow ODEs.

• Pseudo Numerical Methods for Diffusion Models on Manifolds
  arXiv:2202.09778 (ICLR 2022)
  Adapts numerical integration methods to accelerate diffusion sampling.

• Denoising Diffusion Implicit Models
  arXiv:2010.02502 (ICLR 2021)
  Introduces non-Markovian diffusion sampling, including deterministic sampling with fewer steps.

Discrete and language generation

Related background on discrete generative processes; these are not consistency-model papers.

• Block Diffusion: Interpolating Between Autoregressive and Diffusion Language Models
  arXiv:2503.09573
  Combines autoregressive block structure with discrete diffusion, enabling parallel token sampling and variable-length generation.

• Discrete Flow Matching
  arXiv:2407.15595 (arXiv 2024)
  Extends flow matching to discrete state spaces for discrete generative modeling.

Learning resources

• The Fokker Planck Equation and Diffusion Models
  Blog
  Explains the Fokker-Planck equation and its role in diffusion models.

• Generative AI and Foundation Models, Spring 2024 by Ernest K. Ryu
  Course Page
  Course on generative AI and foundation models.

• A Visual Dive into Conditional Flow Matching
  Blog
  Visual explanation of conditional flow matching.

For additional background on reward optimization in language models, see related reading. Those references are kept separate from the consistency-model bibliography.

Contributing

Suggestions and corrections are welcome. Please read the contribution guidelines, then open a pull request or suggest a paper.

Include the exact title, a verified primary paper link, a concise contribution summary, and the most relevant category. Official code and project pages are welcome when available.