# VCT: Training Consistency Models with Variational Noise Coupling arXiv: https://arxiv.org/abs/2502.18197 ยท HTML: https://mlsanity.com/paper/2502.18197/ ## Key facts - Cited by 15 papers in the map (data through 14 Oct 2026). - Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. - Builds on 50 of its 67 references that are in the map. - First posted on arXiv 25 Feb 2025. ## Placed in - Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/) ## Builds on (most cited first, 30 of 50) - [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) - [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020) - [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020) - [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021) - [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015) - [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018) - [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022) - [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017) - [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018) - [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) - [DiffWave: A Versatile Diffusion Model for Audio Synthesis](https://mlsanity.com/paper/2009.09761/) (2020) - [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019) - [One-step Diffusion with Distribution Matching Distillation](https://mlsanity.com/paper/2311.18828/) (2023) - [Building Normalizing Flows with Stochastic Interpolants](https://mlsanity.com/paper/2209.15571/) (2022) - [Improving and generalizing flow-based generative models with minibatch optimal transport](https://mlsanity.com/paper/2302.00482/) (2023) - [Pseudo Numerical Methods for Diffusion Models on Manifolds](https://mlsanity.com/paper/2202.09778/) (2022) - [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) - [Knowledge Distillation in Iterative Generative Models for Improved Sampling Speed](https://mlsanity.com/paper/2101.02388/) (2021) - [Simplifying, Stabilizing and Scaling Continuous-Time Consistency Models](https://mlsanity.com/paper/2410.11081/) (2024) - [Multisample Flow Matching: Straightening Flows with Minibatch Couplings](https://mlsanity.com/paper/2304.14772/) (2023) - [Diff-Instruct: A Universal Approach for Transferring Knowledge From Pre-trained Diffusion Models](https://mlsanity.com/paper/2305.18455/) (2023) - [Gotta Go Fast When Generating Data with Score-Based Models](https://mlsanity.com/paper/2105.14080/) (2021) ## Built on by (most cited first, 15 of 15) - [CMT: Mid-Training for Efficient Learning of Consistency, Mean Flow, and Flow Map Models](https://mlsanity.com/paper/2509.24526/) (2025) - [The Curse of Conditions: Analyzing and Improving Optimal Transport for Conditional Flow-Based Generation](https://mlsanity.com/paper/2503.10636/) (2025) - [An efficient probabilistic hardware architecture for diffusion-like models](https://mlsanity.com/paper/2510.23972/) (2025) - [Learning Straight Flows: Variational Flow Matching for Efficient Generation](https://mlsanity.com/paper/2511.17583/) (2025) - [Variational Flow Maps: Make Some Noise for One-Step Conditional Generation](https://mlsanity.com/paper/2603.07276/) (2026) - [Training Latent Diffusion Models with Interacting Particle Algorithms](https://mlsanity.com/paper/2505.12412/) (2025) - [Midpoint Generative Models](https://mlsanity.com/paper/2605.29920/) (2026) - [CoVAE: Consistency Training of Variational Autoencoders](https://mlsanity.com/paper/2507.09103/) (2025) - [Stabilizing Consistency Training: A Flow Map Analysis and Self-Distillation](https://mlsanity.com/paper/2601.22679/) (2026) - [Hierarchical Koopman Diffusion: Fast Generation with Interpretable Diffusion Trajectory](https://mlsanity.com/paper/2510.12220/) (2025) - [Transition Flow Matching](https://mlsanity.com/paper/2603.15689/) (2026) - [Drift Flow Matching](https://mlsanity.com/paper/2605.17244/) (2026) - [MixFlow: Mixed Source Distributions Improve Rectified Flows](https://mlsanity.com/paper/2604.09181/) (2026) - [One-Sided Quantile Coupling for Flow Matching](https://mlsanity.com/paper/2608.00978/) (2026) - [Structured Coupling for Flow Matching](https://mlsanity.com/paper/2605.07676/) (2026) ## Abstract (arXiv) Consistency Training (CT) has recently emerged as a strong alternative to diffusion models for image generation. However, non-distillation CT often suffers from high variance and instability, motivating ongoing research into its training dynamics. We propose Variational Consistency Training (VCT), a flexible and effective framework compatible with various forward kernels, including those in flow matching. Its key innovation is a learned noise-data coupling scheme inspired by Variational Autoencoders, where a data-dependent encoder models noise emission. This enables VCT to adaptively learn noise-todata pairings, reducing training variance relative to the fixed, unsorted pairings in classical CT. Experiments on multiple image datasets demonstrate significant improvements: our method surpasses baselines, achieves state-of-the-art FID among non-distillation CT approaches on CIFAR-10, and matches SoTA performance on ImageNet 64 x 64 with only two sampling steps. Code is available at https://github.com/sony/vct.