# Test-time scaling of diffusions with flow maps

arXiv: https://arxiv.org/abs/2511.22688 · HTML: https://mlsanity.com/paper/2511.22688/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 31 of its 38 references that are in the map.
- First posted on arXiv 27 Nov 2025.

## Placed in

- Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/)

## Builds on (most cited first, 30 of 31)

- [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)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Qwen2.5-VL Technical Report](https://mlsanity.com/paper/2502.13923/) (2025)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Consistency Models](https://mlsanity.com/paper/2303.01469/) (2023)
- [Concrete Problems in AI Safety](https://mlsanity.com/paper/1606.06565/) (2016)
- [ImageReward: Learning and Evaluating Human Preferences for Text-to-Image Generation](https://mlsanity.com/paper/2304.05977/) (2023)
- [Building Normalizing Flows with Stochastic Interpolants](https://mlsanity.com/paper/2209.15571/) (2022)
- [Pick-a-Pic: An Open Dataset of User Preferences for Text-to-Image Generation](https://mlsanity.com/paper/2305.01569/) (2023)
- [GenEval: An Object-Focused Framework for Evaluating Text-to-Image Alignment](https://mlsanity.com/paper/2310.11513/) (2023)
- [Stochastic Interpolants: A Unifying Framework for Flows and Diffusions](https://mlsanity.com/paper/2303.08797/) (2023)
- [Human Preference Score v2: A Solid Benchmark for Evaluating Human Preferences of Text-to-Image Synthesis](https://mlsanity.com/paper/2306.09341/) (2023)
- [Mean Flows for One-step Generative Modeling](https://mlsanity.com/paper/2505.13447/) (2025)
- [Consistency Trajectory Models: Learning Probability Flow ODE Trajectory of Diffusion](https://mlsanity.com/paper/2310.02279/) (2023)
- [Inference-Time Scaling for Diffusion Models beyond Scaling Denoising Steps](https://mlsanity.com/paper/2501.09732/) (2025)
- [Practical and Asymptotically Exact Conditional Sampling in Diffusion Models](https://mlsanity.com/paper/2306.17775/) (2023)
- [A General Framework for Inference-time Scaling and Steering of Diffusion Models](https://mlsanity.com/paper/2501.06848/) (2025)
- [ReNO: Enhancing One-step Text-to-Image Models through Reward-based Noise Optimization](https://mlsanity.com/paper/2406.04312/) (2024)
- [How to build a consistency model: Learning flow maps via self-distillation](https://mlsanity.com/paper/2505.18825/) (2025)
- [Feynman-Kac Correctors in Diffusion: Annealing, Guidance, and Product of Experts](https://mlsanity.com/paper/2503.02819/) (2025)
- [Align Your Flow: Scaling Continuous-Time Flow Map Distillation](https://mlsanity.com/paper/2506.14603/) (2025)
- [An invitation to sequential Monte Carlo samplers](https://mlsanity.com/paper/2007.11936/) (2020)
- [Skywork-VL Reward: An Effective Reward Model for Multimodal Understanding and Reasoning](https://mlsanity.com/paper/2505.07263/) (2025)
- [Test-Time Scaling of Diffusion Models via Noise Trajectory Search](https://mlsanity.com/paper/2506.03164/) (2025)
- [UniGenBench++: A Unified Semantic Evaluation Benchmark for Text-to-Image Generation](https://mlsanity.com/paper/2510.18701/) (2025)
- [Flow Matching with Semidiscrete Couplings](https://mlsanity.com/paper/2509.25519/) (2025)
- [Adaptive Inference-Time Scaling via Cyclic Diffusion Search](https://mlsanity.com/paper/2505.14036/) (2025)
- [VFScale: Intrinsic Reasoning through Verifier-Free Test-time Scalable Diffusion Model](https://mlsanity.com/paper/2502.01989/) (2025)

## Built on by (most cited first, 16 of 16)

- [Categorical Flow Maps](https://mlsanity.com/paper/2602.12233/) (2026)
- [Diamond Maps: Efficient Reward Alignment via Stochastic Flow Maps](https://mlsanity.com/paper/2602.05993/) (2026)
- [Riemannian MeanFlow](https://mlsanity.com/paper/2602.07744/) (2026)
- [How to Guide Your Flow: Few-Step Alignment via Flow Map Reward Guidance](https://mlsanity.com/paper/2604.27147/) (2026)
- [Inference-Time Alignment for Diffusion Models via Variationally Stable Doob's Matching](https://mlsanity.com/paper/2601.06514/) (2026)
- [Calibrated Test-Time Guidance for Bayesian Inference](https://mlsanity.com/paper/2602.22428/) (2026)
- [Diffusion Reinforcement Learning via Centered Reward Distillation](https://mlsanity.com/paper/2603.14128/) (2026)
- [SURGE: Approximation and Training Free Particle Filter for Diffusion Surrogate](https://mlsanity.com/paper/2605.18745/) (2026)
- [Simple Approximation and Derivative Free Inference-Time Scaling for Diffusion Models via Sequential Monte Carlo on Path Measures](https://mlsanity.com/paper/2605.17850/) (2026)
- [Flow Map Denoisers: Traversing the Distortion-Perception Plane for Inverse Problems](https://mlsanity.com/paper/2606.19802/) (2026)
- [ScoRe-Flow: Complete Distributional Control via Score-Based Reinforcement Learning for Flow Matching](https://mlsanity.com/paper/2604.10962/) (2026)
- [(1D) Ordered Tokens Enable Efficient Test-Time Search](https://mlsanity.com/paper/2604.15453/) (2026)
- [Few-step Cofolding with All-Atom Flow Maps](https://mlsanity.com/paper/2606.08375/) (2026)
- [FluxLite: Inference-Time Proposal Control for Discrete Diffusion Models](https://mlsanity.com/paper/2609.35947/) (2026)
- [Follow the Mean: Reference-Guided Flow Matching](https://mlsanity.com/paper/2605.10302/) (2026)
- [Error-Corrected Inference-Time Scaling for Imperfect Diffusion Models](https://mlsanity.com/paper/2610.01933/) (2026)

## Abstract (arXiv)

A common recipe to improve diffusion models at test-time so that samples score highly against a user-specified reward is to introduce the gradient of the reward into the dynamics of the diffusion itself. This procedure is often ill posed, as user-specified rewards are usually only well defined on the data distribution at the end of generation. While common workarounds to this problem are to use a denoiser to estimate what a sample would have been at the end of generation, we propose a simple solution to this problem by working directly with a flow map. By exploiting a relationship between the flow map and velocity field governing the instantaneous transport, we construct an algorithm, Flow Map Trajectory Tilting (FMTT), which provably performs better ascent on the reward than standard test-time methods involving the gradient of the reward. The approach can be used to either perform exact sampling via importance weighting or principled search that identifies local maximizers of the reward-tilted distribution. We demonstrate the efficacy of our approach against other look-ahead techniques, and show how the flow map enables engagement with complicated reward functions that make possible new forms of image editing, e.g. by interfacing with vision language models.