# Source-Guided Flow Matching arXiv: https://arxiv.org/abs/2508.14807 ยท HTML: https://mlsanity.com/paper/2508.14807/ ## Key facts - Cited by 13 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 32 of its 41 references that are in the map. - First posted on arXiv 20 Aug 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 32) - [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) - [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022) - [Improving and generalizing flow-based generative models with minibatch optimal transport](https://mlsanity.com/paper/2302.00482/) (2023) - [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) - [Adjoint Matching: Fine-tuning Flow and Diffusion Generative Models with Memoryless Stochastic Optimal Control](https://mlsanity.com/paper/2409.08861/) (2024) - [Practical and Asymptotically Exact Conditional Sampling in Diffusion Models](https://mlsanity.com/paper/2306.17775/) (2023) - [Diffusion models as plug-and-play priors](https://mlsanity.com/paper/2206.09012/) (2022) - [Reduce, Reuse, Recycle: Compositional Generation with Energy-Based Diffusion Models and MCMC](https://mlsanity.com/paper/2302.11552/) (2023) - [Fine-Tuning of Continuous-Time Diffusion Models as Entropy-Regularized Control](https://mlsanity.com/paper/2402.15194/) (2024) - [D-Flow: Differentiating through Flows for Controlled Generation](https://mlsanity.com/paper/2402.14017/) (2024) - [End-to-End Diffusion Latent Optimization Improves Classifier Guidance](https://mlsanity.com/paper/2303.13703/) (2023) - [TFG: Unified Training-Free Guidance for Diffusion Models](https://mlsanity.com/paper/2409.15761/) (2024) - [Guided Flows for Generative Modeling and Decision Making](https://mlsanity.com/paper/2311.13443/) (2023) - [Optimizing Diffusion Noise Can Serve As Universal Motion Priors](https://mlsanity.com/paper/2312.11994/) (2023) - [PnP-Flow: Plug-and-Play Image Restoration with Flow Matching](https://mlsanity.com/paper/2410.02423/) (2024) - [Error Bounds for Flow Matching Methods](https://mlsanity.com/paper/2305.16860/) (2023) - [Physics-Informed Diffusion Models](https://mlsanity.com/paper/2403.14404/) (2024) - [Optimal Flow Matching: Learning Straight Trajectories in Just One Step](https://mlsanity.com/paper/2403.13117/) (2024) - [DITTO: Diffusion Inference-Time T-Optimization for Music Generation](https://mlsanity.com/paper/2401.12179/) (2024) - [Provably Robust Score-Based Diffusion Posterior Sampling for Plug-and-Play Image Reconstruction](https://mlsanity.com/paper/2403.17042/) (2024) - [Gradient Guidance for Diffusion Models: An Optimization Perspective](https://mlsanity.com/paper/2404.14743/) (2024) - [CoCoGen: Physically-Consistent and Conditioned Score-based Generative Models for Forward and Inverse Problems](https://mlsanity.com/paper/2312.10527/) (2023) - [Inference-Time Alignment of Diffusion Models with Direct Noise Optimization](https://mlsanity.com/paper/2405.18881/) (2024) - [On the Guidance of Flow Matching](https://mlsanity.com/paper/2502.02150/) (2025) - [Fine-tuning of diffusion models via stochastic control: entropy regularization and beyond](https://mlsanity.com/paper/2403.06279/) (2024) ## Built on by (most cited first, 13 of 13) - [ESS-Flow: Training-free guidance of flow-based models as inference in source space](https://mlsanity.com/paper/2510.05849/) (2025) - [D-Flow SGLD: Source-Space Posterior Sampling for Scientific Inverse Problems with Flow Matching](https://mlsanity.com/paper/2602.21469/) (2026) - [Discrete diffusion samplers and bridges: Off-policy algorithms and applications in latent spaces](https://mlsanity.com/paper/2602.05961/) (2026) - [The Right Measure for Physics-Constrained Generation: A Co-Area Correction for Posterior-Consistent PDE Inverse Problems](https://mlsanity.com/paper/2606.04804/) (2026) - [LatentFlow: A General Framework for Conditioning Stochastic Processes](https://mlsanity.com/paper/2607.12922/) (2026) - [Contact Wasserstein Geodesics for Non-Conservative Schr"odinger Bridges](https://mlsanity.com/paper/2511.06856/) (2025) - [Na"ive PAINE: Lightweight Text-to-Image Generation Improvement with Prompt Evaluation](https://mlsanity.com/paper/2603.12506/) (2026) - [Conflict-Aware Additive Guidance for Flow Models under Compositional Rewards](https://mlsanity.com/paper/2605.20758/) (2026) - [Can We Predict The Human Preference For Text-to-Image Content Prior To Generation And Is It Even Useful To Do So?](https://mlsanity.com/paper/2606.05478/) (2026) - [Alternating Levenberg-Marquardt Training of Physics-Informed Neural Networks with Fourier-Enhanced Features](https://mlsanity.com/paper/2608.05892/) (2026) - [Interacting particle guidance for sampling reward-tilted generative priors](https://mlsanity.com/paper/2609.37227/) (2026) - [Posterior sampling by source-space MCMC via prior-based few-step transport maps](https://mlsanity.com/paper/2610.01034/) (2026) - [Amortised Inference through One-Step Implicit Sampling](https://mlsanity.com/paper/2610.12679/) (2026) ## Abstract (arXiv) Guidance of generative models is typically achieved by modifying the probability flow vector field through the addition of a guidance field. In this paper, we instead propose the Source-Guided Flow Matching (SGFM) framework, which modifies the source distribution directly while keeping the pre-trained vector field intact. This reduces the guidance problem to a well-defined problem of sampling from the source distribution. We theoretically show that SGFM recovers the desired target distribution exactly. Furthermore, we provide bounds on the Wasserstein error for the generated distribution when using an approximate sampler of the source distribution and an approximate vector field. The key benefit of our approach is that it allows the user to flexibly choose the sampling method depending on their specific problem. To illustrate this, we systematically compare different sampling methods and discuss conditions for asymptotically exact guidance. Moreover, our framework integrates well with optimal flow matching models since the straight transport map generated by the vector field is preserved. Experimental results on synthetic 2D benchmarks, physics-informed generative tasks, and imaging inverse problems demonstrate the effectiveness and flexibility of the proposed framework.