# Efficient Flow Matching using Latent Variables

arXiv: https://arxiv.org/abs/2505.04486 · HTML: https://mlsanity.com/paper/2505.04486/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 30 of its 58 references that are in the map.
- First posted on arXiv 7 May 2025.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

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

- [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)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [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)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Understanding deep learning requires rethinking generalization](https://mlsanity.com/paper/1611.03530/) (2016)
- [Stochastic Interpolants: A Unifying Framework for Flows and Diffusions](https://mlsanity.com/paper/2303.08797/) (2023)
- [Improving and generalizing flow-based generative models with minibatch optimal transport](https://mlsanity.com/paper/2302.00482/) (2023)
- [SiT: Exploring Flow and Diffusion-based Generative Models with Scalable Interpolant Transformers](https://mlsanity.com/paper/2401.08740/) (2024)
- [NVAE: A Deep Hierarchical Variational Autoencoder](https://mlsanity.com/paper/2007.03898/) (2020)
- [Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modeling](https://mlsanity.com/paper/2106.01357/) (2021)
- [Stronger generalization bounds for deep nets via a compression approach](https://mlsanity.com/paper/1802.05296/) (2018)
- [Multisample Flow Matching: Straightening Flows with Minibatch Couplings](https://mlsanity.com/paper/2304.14772/) (2023)
- [Understanding and Mitigating Copying in Diffusion Models](https://mlsanity.com/paper/2305.20086/) (2023)
- [TrajectoryNet: A Dynamic Optimal Transport Network for Modeling Cellular Dynamics](https://mlsanity.com/paper/2002.04461/) (2020)
- [Patch Diffusion: Faster and More Data-Efficient Training of Diffusion Models](https://mlsanity.com/paper/2304.12526/) (2023)
- [On Memorization in Diffusion Models](https://mlsanity.com/paper/2310.02664/) (2023)
- [Soft Diffusion: Score Matching for General Corruptions](https://mlsanity.com/paper/2209.05442/) (2022)
- [CoCoGen: Physically-Consistent and Conditioned Score-based Generative Models for Forward and Inverse Problems](https://mlsanity.com/paper/2312.10527/) (2023)
- [FlowLLM: Flow Matching for Material Generation with Large Language Models as Base Distributions](https://mlsanity.com/paper/2410.23405/) (2024)
- [Flow Matching with Gaussian Process Priors for Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2410.03024/) (2024)
- [ET-Flow: Equivariant Flow-Matching for Molecular Conformer Generation](https://mlsanity.com/paper/2410.22388/) (2024)
- [Variational Rectified Flow Matching](https://mlsanity.com/paper/2502.09616/) (2025)
- [A Differential Entropy Estimator for Training Neural Networks](https://mlsanity.com/paper/2202.06618/) (2022)
- [Mechanisms of Projective Composition of Diffusion Models](https://mlsanity.com/paper/2502.04549/) (2025)
- [Structured Diffusion Models with Mixture of Gaussians as Prior Distribution](https://mlsanity.com/paper/2410.19149/) (2024)
- [REMEDI: Corrective Transformations for Improved Neural Entropy Estimation](https://mlsanity.com/paper/2402.05718/) (2024)

## Built on by (most cited first, 6 of 6)

- [VFP: Variational Flow-Matching Policy for Multi-Modal Robot Manipulation](https://mlsanity.com/paper/2508.01622/) (2025)
- [Generative Modeling of Discrete Data Using Geometric Latent Subspaces](https://mlsanity.com/paper/2601.21831/) (2026)
- [All-Atom GPCR-Ligand Dynamics Simulation via a Residual Latent Flow Mode](https://mlsanity.com/paper/2602.03902/) (2026)
- [Uncovering Physical Drivers of Dark Matter Halo Structures with Auxiliary-Variable-Guided Generative Models](https://mlsanity.com/paper/2602.23518/) (2026)
- [Towards Faster Language Model Inference Using Mixture-of-Experts Flow Matching](https://mlsanity.com/paper/2604.15009/) (2026)
- [Representation Learning in Diffusion and Flow-based Model: An Application Aspect](https://mlsanity.com/paper/2608.24068/) (2026)

## Abstract (arXiv)

Flow matching models have shown great potential in image generation tasks among probabilistic generative models. However, most flow matching models in the literature do not explicitly utilize the underlying clustering structure in the target data when learning the flow from a simple source distribution like the standard Gaussian. This leads to inefficient learning, especially for many high-dimensional real-world datasets, which often reside in a low-dimensional manifold. To this end, we present textttLatent-CFM, which provides efficient training strategies by conditioning on the features extracted from data using pretrained deep latent variable models. Through experiments on synthetic data from multi-modal distributions and widely used image benchmark datasets, we show that textttLatent-CFM exhibits improved generation quality with significantly less training and computation than state-of-the-art flow matching models by adopting pretrained lightweight latent variable models. Beyond natural images, we consider generative modeling of spatial fields stemming from physical processes. Using a 2d Darcy flow dataset, we demonstrate that our approach generates more physically accurate samples than competing approaches. In addition, through latent space analysis, we demonstrate that our approach can be used for conditional image generation conditioned on latent features, which adds interpretability to the generation process.