# Is There a Better Source Distribution than Gaussian? Exploring Source Distributions for Image Flow Matching arXiv: https://arxiv.org/abs/2512.18184 ยท HTML: https://mlsanity.com/paper/2512.18184/ ## Key facts - Cited by 5 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 45 of its 60 references that are in the map. - First posted on arXiv 20 Dec 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 45) - [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020) - [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015) - [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) - [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022) - [SDXL: Improving Latent Diffusion Models for High-Resolution Image Synthesis](https://mlsanity.com/paper/2307.01952/) (2023) - [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024) - [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019) - [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018) - [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021) - [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022) - [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) - [Movie Gen: A Cast of Media Foundation Models](https://mlsanity.com/paper/2410.13720/) (2024) - [FFJORD: Free-form Continuous Dynamics for Scalable Reversible Generative Models](https://mlsanity.com/paper/1810.01367/) (2018) - [Diffusion Autoencoders: Toward a Meaningful and Decodable Representation](https://mlsanity.com/paper/2111.15640/) (2021) - [Reconstruction vs. Generation: Taming Optimization Dilemma in Latent Diffusion Models](https://mlsanity.com/paper/2501.01423/) (2025) - [Pyramidal Flow Matching for Efficient Video Generative Modeling](https://mlsanity.com/paper/2410.05954/) (2024) - [Discrete Flow Matching](https://mlsanity.com/paper/2407.15595/) (2024) - [Multisample Flow Matching: Straightening Flows with Minibatch Couplings](https://mlsanity.com/paper/2304.14772/) (2023) - [Flow Matching on General Geometries](https://mlsanity.com/paper/2302.03660/) (2023) - [Deep Compression Autoencoder for Efficient High-Resolution Diffusion Models](https://mlsanity.com/paper/2410.10733/) (2024) - [Latent Space Oddity: on the Curvature of Deep Generative Models](https://mlsanity.com/paper/1710.11379/) (2017) - [Flow Matching in Latent Space](https://mlsanity.com/paper/2307.08698/) (2023) - [Dirichlet Flow Matching with Applications to DNA Sequence Design](https://mlsanity.com/paper/2402.05841/) (2024) - [AlphaFold Meets Flow Matching for Generating Protein Ensembles](https://mlsanity.com/paper/2402.04845/) (2024) - [Masked Autoencoders Are Effective Tokenizers for Diffusion Models](https://mlsanity.com/paper/2502.03444/) (2025) ## Built on by (most cited first, 5 of 5) - [Better Source, Better Flow: Learning Condition-Dependent Source Distribution for Flow Matching](https://mlsanity.com/paper/2602.05951/) (2026) - [Spatially-Grounded Flow Matching: Structured Source Distributions for Image Generation](https://mlsanity.com/paper/2608.15452/) (2026) - [Flow Matching with Optimized Subclass Priors for Medical Image Augmentation](https://mlsanity.com/paper/2605.16469/) (2026) - [Beyond the Manifold Hypothesis: Hybrid Spectral Parameterizations for Flow Matching](https://mlsanity.com/paper/2609.32432/) (2026) - [Learning Conditional Source Distribution via Flow Reversal for Temporal Flow Matching](https://mlsanity.com/paper/2610.05349/) (2026) ## Abstract (arXiv) Flow matching has emerged as a powerful generative modeling approach with flexible choices of source distribution. While Gaussian distributions are commonly used, the potential for better alternatives in high-dimensional data generation remains largely unexplored. In this paper, we propose a novel 2D simulation that captures high-dimensional geometric properties in an interpretable 2D setting, enabling us to analyze the learning dynamics of flow matching during training. Based on this analysis, we derive several key insights about flow matching behavior: (1) density approximation can paradoxically degrade performance due to mode discrepancy, (2) directional alignment suffers from path entanglement when overly concentrated, (3) Gaussian's omnidirectional coverage ensures robust learning, and (4) norm misalignment incurs substantial learning costs. Building on these insights, we propose a practical framework that combines norm-aligned training with directionally-pruned sampling. This approach maintains the robust omnidirectional supervision essential for stable flow learning, while eliminating initializations in data-sparse regions during inference. Importantly, our pruning strategy can be applied to any flow matching model trained with a Gaussian source, providing immediate performance gains without the need for retraining. Empirical evaluations demonstrate consistent improvements in both generation quality and sampling efficiency. Our findings provide practical insights and guidelines for source distribution design and introduce a readily applicable technique for improving existing flow matching models. Our code is available at https://github.com/kwanseokk/SourceFM.