# Better Source, Better Flow: Learning Condition-Dependent Source Distribution for Flow Matching arXiv: https://arxiv.org/abs/2602.05951 · HTML: https://mlsanity.com/paper/2602.05951/ ## Key facts - Cited by 9 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 65 of its 72 references that are in the map. - First posted on arXiv 5 Feb 2026. ## 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 65) - [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014) - [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021) - [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020) - [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) - [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025) - [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014) - [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021) - [DINOv2: Learning Robust Visual Features without Supervision](https://mlsanity.com/paper/2304.07193/) (2023) - [Emerging Properties in Self-Supervised Vision Transformers](https://mlsanity.com/paper/2104.14294/) (2021) - [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022) - [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022) - [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022) - [Qwen2.5-VL Technical Report](https://mlsanity.com/paper/2502.13923/) (2025) - [Bootstrap your own latent: A new approach to self-supervised Learning](https://mlsanity.com/paper/2006.07733/) (2020) - [BLIP: Bootstrapping Language-Image Pre-training for Unified Vision-Language Understanding and Generation](https://mlsanity.com/paper/2201.12086/) (2022) - [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024) - [LAION-5B: An open large-scale dataset for training next generation image-text models](https://mlsanity.com/paper/2210.08402/) (2022) - [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019) - [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022) - [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016) - [Qwen3-VL Technical Report](https://mlsanity.com/paper/2511.21631/) (2025) - [CLIPScore: A Reference-free Evaluation Metric for Image Captioning](https://mlsanity.com/paper/2104.08718/) (2021) - [SigLIP 2: Multilingual Vision-Language Encoders with Improved Semantic Understanding, Localization, and Dense Features](https://mlsanity.com/paper/2502.14786/) (2025) - [GenEval: An Object-Focused Framework for Evaluating Text-to-Image Alignment](https://mlsanity.com/paper/2310.11513/) (2023) - [Improving and generalizing flow-based generative models with minibatch optimal transport](https://mlsanity.com/paper/2302.00482/) (2023) - [PixArt-α: Fast Training of Diffusion Transformer for Photorealistic Text-to-Image Synthesis](https://mlsanity.com/paper/2310.00426/) (2023) - [Representation Alignment for Generation: Training Diffusion Transformers Is Easier Than You Think](https://mlsanity.com/paper/2410.06940/) (2024) - [T2M-GPT: Generating Human Motion from Textual Descriptions with Discrete Representations](https://mlsanity.com/paper/2301.06052/) (2023) - [ELLA: Equip Diffusion Models with LLM for Enhanced Semantic Alignment](https://mlsanity.com/paper/2403.05135/) (2024) ## Built on by (most cited first, 9 of 9) - [Optimal Transport Flow Matching by Design](https://mlsanity.com/paper/2606.04092/) (2026) - [Spatially-Grounded Flow Matching: Structured Source Distributions for Image Generation](https://mlsanity.com/paper/2608.15452/) (2026) - [Flow Matching with Arbitrary Auxiliary Paths](https://mlsanity.com/paper/2605.06364/) (2026) - [Flow Matching with Optimized Subclass Priors for Medical Image Augmentation](https://mlsanity.com/paper/2605.16469/) (2026) - [Flow-JEPA: Flow Matching for Robust Latent Dynamics in JEPA World Models](https://mlsanity.com/paper/2608.29029/) (2026) - [Beyond Random Couplings: Contrastive Noise Alignment in Generative Flows](https://mlsanity.com/paper/2609.18488/) (2026) - [Beyond the Manifold Hypothesis: Hybrid Spectral Parameterizations for Flow Matching](https://mlsanity.com/paper/2609.32432/) (2026) - [GRFBrain: Graph-Structured Rectified Flows for EEG Dynamic Modeling](https://mlsanity.com/paper/2609.37934/) (2026) - [Learning Conditional Source Distribution via Flow Reversal for Temporal Flow Matching](https://mlsanity.com/paper/2610.05349/) (2026) ## Abstract (arXiv) Flow matching has recently emerged as a promising alternative to diffusion-based generative models, particularly for text-to-image generation. Despite its flexibility in allowing arbitrary source distributions, most existing approaches rely on a standard Gaussian distribution, a choice inherited from diffusion models, and rarely consider the source distribution itself as an optimization target in such settings. In this work, we show that principled design of the source distribution is not only feasible but also beneficial at the scale of modern text-to-image systems. Specifically, we propose learning a condition-dependent source distribution under flow matching objective that better exploit rich conditioning signals. We identify key failure modes that arise when directly incorporating conditioning into the source, including distributional collapse and instability, and show that appropriate variance regularization and directional alignment between source and target are critical for stable and effective learning. We further analyze how the choice of target representation space impacts flow matching with structured sources, revealing regimes in which such designs are most effective. Extensive experiments across multiple text-to-image benchmarks demonstrate consistent and robust improvements, including up to a 3x faster convergence in FID, highlighting the practical benefits of a principled source distribution design for conditional flow matching.