Bidirectional Consistency Models
On the map: Diffusion models → Diffusion foundations and sampling
Abstract (arXiv)
Diffusion models (DMs) are capable of generating remarkably high-quality samples by iteratively denoising a random vector, a process that corresponds to moving along the probability flow ordinary differential equation (PF ODE). Interestingly, DMs can also invert an input image to noise by moving backward along the PF ODE, a key operation for downstream tasks such as interpolation and image editing. However, the iterative nature of this process restricts its speed, hindering its broader application. Recently, Consistency Models (CMs) have emerged to address this challenge by approximating the integral of the PF ODE, largely reducing the number of iterations. Yet, the absence of an explicit ODE solver complicates the inversion process. To resolve this, we introduce Bidirectional Consistency Model (BCM), which learns a single neural network that enables both forward and backward traversal along the PF ODE, efficiently unifying generation and inversion tasks within one framework. We can train BCM from scratch or tune it using a pretrained consistency model, which reduces the training cost and increases scalability. We demonstrate that BCM enables one-step generation and inversion while also allowing the use of additional steps to enhance generation quality or reduce reconstruction error. We further showcase BCM's capability in downstream tasks, such as interpolation and inpainting. Our code and weights are available at https://github.com/Mosasaur5526/BCM-iCT-torch.
Key facts. Cited by 18 papers in the map (data through 7 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 54 of its 70 references that are in the map. First posted on arXiv 26 Mar 2024.
Builds on
54 of 70 references.
Closest ancestors · 19
Same direction, newest first
- 2023Analyzing and Improving the Training Dynamics of Diffusion Models5 Dec
- 2023Fast ODE-based Sampling for Diffusion Models in Around 5 Steps30 Nov
- 2023Improved Techniques for Training Consistency Models22 Oct
- 2023Latent Consistency Models: Synthesizing High-Resolution Images with Few-Step Inference6 Oct
- 2023Consistency Trajectory Models: Learning Probability Flow ODE Trajectory of Diffusion1 Oct
- 2023Convergence guarantee for consistency models22 Aug
- 2023Diff-Instruct: A Universal Approach for Transferring Knowledge From Pre-trained Diffusion Models29 May
- 2023Consistency Models2 Mar
- 2023I2SB: Image-to-Image Schr"odinger Bridge12 Feb
- 2022Fast Sampling of Diffusion Models via Operator Learning24 Nov
- 2022DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps2 Jun
- 2022Elucidating the Design Space of Diffusion-Based Generative Models1 Jun
7 more
- 2022Fast Sampling of Diffusion Models with Exponential Integrator29 Apr
- 2021High-Resolution Image Synthesis with Latent Diffusion Models20 Dec
- 2021Diffusion Models Beat GANs on Image Synthesis11 May
- 2021Knowledge Distillation in Iterative Generative Models for Improved Sampling Speed7 Jan
- 2020Score-Based Generative Modeling through Stochastic Differential Equations26 Nov
- 2020Denoising Diffusion Implicit Models6 Oct
- 2020Denoising Diffusion Probabilistic Models19 Jun
Other references · 35
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Citing papers per year: 2024: 8; 2025: 8; 2026: 2.
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- 2024Flow map matching with stochastic interpolants: A mathematical framework for consistency modelscited by 99
- 2025How to build a consistency model: Learning flow maps via self-distillationcited by 96
- 2025Align Your Flow: Scaling Continuous-Time Flow Map Distillationcited by 81
- 2024BELM: Bidirectional Explicit Linear Multi-step Sampler for Exact Inversion in Diffusion Modelscited by 29
- 2024Consistency Diffusion Bridge Modelscited by 22
- 2024Invertible Consistency Distillation for Text-Guided Image Editing in Around 7 Stepscited by 14
- 2024Improving Probabilistic Diffusion Models With Optimal Diagonal Covariance Matchingcited by 13
- 2024PostEdit: Posterior Sampling for Efficient Zero-Shot Image Editingcited by 9
- 2025DiffRatio: Training One-Step Diffusion Models Without Teacher Supervisioncited by 8
- 2026How to Guide Your Flow: Few-Step Alignment via Flow Map Reward Guidancecited by 5
- 2025Single-Step Bidirectional Unpaired Image Translation Using Implicit Bridge Consistency Distillationcited by 4
- 2024Efficient and Unbiased Sampling of Boltzmann Distributions via Consistency Modelscited by 2
6 more
- 2025DEFT-VTON: Efficient Virtual Try-On with Consistent Generalised H-Transformcited by 2
- 2025Elucidating the Preconditioning in Consistency Distillationcited by 1
- 2025Beyond and Free from Diffusion: Invertible Guided Consistency Trainingcited by 1
- 2025VarDiU: A Variational Diffusive Upper Bound for One-Step Diffusion Distillationcited by 1
- 2026BiFM: Bidirectional Flow Matching for Few-Step Image Editing and Generationcited by 1
- 2024Inconsistencies In Consistency Models: Better ODE Solving Does Not Imply Better Samplescited by 0
- 2026How to Guide Your Flow: Few-Step Alignment via Flow Map Reward Guidance29 Apr 2026
- 2026BiFM: Bidirectional Flow Matching for Few-Step Image Editing and Generation26 Mar 2026
- 2025DEFT-VTON: Efficient Virtual Try-On with Consistent Generalised H-Transform16 Sep 2025
- 2025VarDiU: A Variational Diffusive Upper Bound for One-Step Diffusion Distillation28 Aug 2025
- 2025Align Your Flow: Scaling Continuous-Time Flow Map Distillation17 Jun 2025
- 2025How to build a consistency model: Learning flow maps via self-distillation24 May 2025
- 2025Single-Step Bidirectional Unpaired Image Translation Using Implicit Bridge Consistency Distillation19 Mar 2025
- 2025DiffRatio: Training One-Step Diffusion Models Without Teacher Supervision11 Feb 2025
- 2025Beyond and Free from Diffusion: Invertible Guided Consistency Training8 Feb 2025
- 2025Elucidating the Preconditioning in Consistency Distillation5 Feb 2025
- 2024Inconsistencies In Consistency Models: Better ODE Solving Does Not Imply Better Samples13 Nov 2024
- 2024Consistency Diffusion Bridge Models30 Oct 2024
6 more
- 2024BELM: Bidirectional Explicit Linear Multi-step Sampler for Exact Inversion in Diffusion Models9 Oct 2024
- 2024PostEdit: Posterior Sampling for Efficient Zero-Shot Image Editing7 Oct 2024
- 2024Efficient and Unbiased Sampling of Boltzmann Distributions via Consistency Models11 Sep 2024
- 2024Invertible Consistency Distillation for Text-Guided Image Editing in Around 7 Steps20 Jun 2024
- 2024Improving Probabilistic Diffusion Models With Optimal Diagonal Covariance Matching16 Jun 2024
- 2024Flow map matching with stochastic interpolants: A mathematical framework for consistency models11 Jun 2024
- 2024Flow map matching with stochastic interpolants: A mathematical framework for consistency modelscited by 99
- 2025How to build a consistency model: Learning flow maps via self-distillationcited by 96
- 2025Align Your Flow: Scaling Continuous-Time Flow Map Distillationcited by 81
- 2024BELM: Bidirectional Explicit Linear Multi-step Sampler for Exact Inversion in Diffusion Modelscited by 29
- 2024Consistency Diffusion Bridge Modelscited by 22
- 2024Invertible Consistency Distillation for Text-Guided Image Editing in Around 7 Stepscited by 14
- 2024Improving Probabilistic Diffusion Models With Optimal Diagonal Covariance Matchingcited by 13
- 2025DiffRatio: Training One-Step Diffusion Models Without Teacher Supervisioncited by 8
- 2024Efficient and Unbiased Sampling of Boltzmann Distributions via Consistency Modelscited by 2
- 2025DEFT-VTON: Efficient Virtual Try-On with Consistent Generalised H-Transformcited by 2
- 2025Elucidating the Preconditioning in Consistency Distillationcited by 1
- 2025Beyond and Free from Diffusion: Invertible Guided Consistency Trainingcited by 1
12 most cited of 15 All 15 (JSON)
- 2026BiFM: Bidirectional Flow Matching for Few-Step Image Editing and Generation26 Mar 2026
- 2025DEFT-VTON: Efficient Virtual Try-On with Consistent Generalised H-Transform16 Sep 2025
- 2025VarDiU: A Variational Diffusive Upper Bound for One-Step Diffusion Distillation28 Aug 2025
- 2025Align Your Flow: Scaling Continuous-Time Flow Map Distillation17 Jun 2025
- 2025How to build a consistency model: Learning flow maps via self-distillation24 May 2025
- 2025DiffRatio: Training One-Step Diffusion Models Without Teacher Supervision11 Feb 2025
- 2025Beyond and Free from Diffusion: Invertible Guided Consistency Training8 Feb 2025
- 2025Elucidating the Preconditioning in Consistency Distillation5 Feb 2025
- 2024Inconsistencies In Consistency Models: Better ODE Solving Does Not Imply Better Samples13 Nov 2024
- 2024Consistency Diffusion Bridge Models30 Oct 2024
- 2024BELM: Bidirectional Explicit Linear Multi-step Sampler for Exact Inversion in Diffusion Models9 Oct 2024
- 2024Efficient and Unbiased Sampling of Boltzmann Distributions via Consistency Models11 Sep 2024
12 newest of 15 All 15 (JSON)
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- 2024Truncated Consistency Models
- 2025PnP-CM: Consistency Models as Plug-and-Play Priors for Inverse Problems
- 2026Consistent Diffusion Language Models
- 2024SCott: Accelerating Diffusion Models with Stochastic Consistency Distillation
- 2024Deep Data Consistency: a Fast and Robust Diffusion Model-based Solver for Inverse Problems
- 2024Consistency Purification: Effective and Efficient Diffusion Purification towards Certified Robustness
- 2026Dual-End Consistency Model
- 2024SITCOM: Step-wise Triple-Consistent Diffusion Sampling for Inverse Problems