# Inference-Time Scaling for Flow Models via Stochastic Generation and Rollover Budget Forcing

arXiv: https://arxiv.org/abs/2503.19385 · HTML: https://mlsanity.com/paper/2503.19385/

## Key facts

- Cited by 38 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion reasoning and test-time scaling, one of 17 directions in LLM reasoning.
- Builds on 65 of its 74 references that are in the map.
- First posted on arXiv 25 Mar 2025.

## Placed in

- LLM reasoning / [Diffusion reasoning and test-time scaling](https://mlsanity.com/lr/diffusion-reasoning-and-test-time-scaling/)
- Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/)

## Builds on (most cited first, 30 of 65)

- [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)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [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)
- [Segment Anything](https://mlsanity.com/paper/2304.02643/) (2023)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Qwen Technical Report](https://mlsanity.com/paper/2309.16609/) (2023)
- [Grounding DINO: Marrying DINO with Grounded Pre-Training for Open-Set Object Detection](https://mlsanity.com/paper/2303.05499/) (2023)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [InstructBLIP: Towards General-purpose Vision-Language Models with Instruction Tuning](https://mlsanity.com/paper/2305.06500/) (2023)
- [Learning to summarize from human feedback](https://mlsanity.com/paper/2009.01325/) (2020)
- [DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps](https://mlsanity.com/paper/2206.00927/) (2022)
- [SDEdit: Guided Image Synthesis and Editing with Stochastic Differential Equations](https://mlsanity.com/paper/2108.01073/) (2021)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [s1: Simple test-time scaling](https://mlsanity.com/paper/2501.19393/) (2025)
- [Variational Diffusion Models](https://mlsanity.com/paper/2107.00630/) (2021)
- [ImageReward: Learning and Evaluating Human Preferences for Text-to-Image Generation](https://mlsanity.com/paper/2304.05977/) (2023)
- [Training Diffusion Models with Reinforcement Learning](https://mlsanity.com/paper/2305.13301/) (2023)
- [Pick-a-Pic: An Open Dataset of User Preferences for Text-to-Image Generation](https://mlsanity.com/paper/2305.01569/) (2023)
- [Stochastic Interpolants: A Unifying Framework for Flows and Diffusions](https://mlsanity.com/paper/2303.08797/) (2023)
- [Diffusion Model Alignment Using Direct Preference Optimization](https://mlsanity.com/paper/2311.12908/) (2023)

## Built on by (most cited first, 30 of 38)

- [Flow-GRPO: Training Flow Matching Models via Online RL](https://mlsanity.com/paper/2505.05470/) (2025)
- [Scaling Image and Video Generation via Test-Time Evolutionary Search](https://mlsanity.com/paper/2505.17618/) (2025)
- [Test-Time Scaling of Diffusion Models via Noise Trajectory Search](https://mlsanity.com/paper/2506.03164/) (2025)
- [GARDO: Reinforcing Diffusion Models without Reward Hacking](https://mlsanity.com/paper/2512.24138/) (2025)
- [Psi-Sampler: Initial Particle Sampling for SMC-Based Inference-Time Reward Alignment in Score Models](https://mlsanity.com/paper/2506.01320/) (2025)
- [Improving Diffusion Language Model Decoding through Joint Search in Generation Order and Token Space](https://mlsanity.com/paper/2601.20339/) (2026)
- [Inference-Time Scaling of Diffusion Language Models via Trajectory Refinement](https://mlsanity.com/paper/2507.08390/) (2025)
- [B'ezierFlow: Learning B'ezier Stochastic Interpolant Schedulers for Few-Step Generation](https://mlsanity.com/paper/2512.13255/) (2025)
- [Scale Where It Matters: Training-Free Localized Scaling for Diffusion Models](https://mlsanity.com/paper/2511.19917/) (2025)
- [Reward-Guided Discrete Diffusion via Clean-Sample Markov Chain for Molecule and Biological Sequence Design](https://mlsanity.com/paper/2602.09424/) (2026)
- [GVCC: Zero-Shot Video Compression via Codebook-Driven Stochastic Rectified Flow](https://mlsanity.com/paper/2603.26571/) (2026)
- [Contrastive Distribution Matching for Amortized Sequential Monte Carlo in Discrete Diffusion](https://mlsanity.com/paper/2605.23346/) (2026)
- [Diffusion Alignment as Variational Expectation-Maximization](https://mlsanity.com/paper/2510.00502/) (2025)
- [Coupled Diffusion Sampling for Training-Free Multi-View Image Editing](https://mlsanity.com/paper/2510.14981/) (2025)
- [MolGuidance: Advanced Guidance Strategies for Conditional Molecular Generation with Flow Matching](https://mlsanity.com/paper/2512.12198/) (2025)
- [Tiny Inference-Time Scaling with Latent Verifiers](https://mlsanity.com/paper/2603.22492/) (2026)
- [Inference-Time Scaling for Joint Audio-Video Generation](https://mlsanity.com/paper/2606.03183/) (2026)
- [FLOWR.root: A flow matching based foundation model for joint multi-purpose structure-aware 3D ligand generation and affinity prediction](https://mlsanity.com/paper/2510.02578/) (2025)
- [Drifting Field Policy: A One-Step Generative Policy via Wasserstein Gradient Flow](https://mlsanity.com/paper/2605.07727/) (2026)
- [Navigating the Exploration-Exploitation Tradeoff in Inference-Time Scaling of Diffusion Models](https://mlsanity.com/paper/2508.12361/) (2025)
- [CARINOX: Inference-time Scaling with Category-Aware Reward-based Initial Noise Optimization and Exploration](https://mlsanity.com/paper/2509.17458/) (2025)
- [Gradient Preconditioning for Efficient and Reliable Reward-Guided Generation](https://mlsanity.com/paper/2602.08646/) (2026)
- [Stitched Value Model for Diffusion Alignment](https://mlsanity.com/paper/2605.19804/) (2026)
- [Visual Autoregressive Models Beat Diffusion Models on Inference Time Scaling](https://mlsanity.com/paper/2510.16751/) (2025)
- [Inference-Time Compute Scaling For Flow Matching](https://mlsanity.com/paper/2510.17786/) (2025)
- [Rethinking Test Time Scaling for Flow-Matching Generative Models](https://mlsanity.com/paper/2511.22242/) (2025)
- [Verifier Threshold: An Efficient Test-Time Scaling Approach for Image Generation](https://mlsanity.com/paper/2512.08985/) (2025)
- [Tuning Real-World Image Restoration at Inference: A Test-Time Scaling Paradigm for Flow Matching Models](https://mlsanity.com/paper/2603.22027/) (2026)
- [NoiseRater: Meta-Learned Noise Valuation for Diffusion Model Training](https://mlsanity.com/paper/2605.08144/) (2026)
- [Don't Settle at the Mode! Mitigating Diversity Collapse in Pretrained Flow Models via Feature Self-Guidance](https://mlsanity.com/paper/2606.27371/) (2026)

## Abstract (arXiv)

We propose an inference-time scaling approach for pretrained flow models. Recently, inference-time scaling has gained significant attention in LLMs and diffusion models, improving sample quality or better aligning outputs with user preferences by leveraging additional computation. For diffusion models, particle sampling has allowed more efficient scaling due to the stochasticity at intermediate denoising steps. On the contrary, while flow models have gained popularity as an alternative to diffusion models--offering faster generation and high-quality outputs in state-of-the-art image and video generative models--efficient inference-time scaling methods used for diffusion models cannot be directly applied due to their deterministic generative process. To enable efficient inference-time scaling for flow models, we propose three key ideas: 1) SDE-based generation, enabling particle sampling in flow models, 2) Interpolant conversion, broadening the search space and enhancing sample diversity, and 3) Rollover Budget Forcing (RBF), an adaptive allocation of computational resources across timesteps to maximize budget utilization. Our experiments show that SDE-based generation, particularly variance-preserving (VP) interpolant-based generation, improves the performance of particle sampling methods for inference-time scaling in flow models. Additionally, we demonstrate that RBF with VP-SDE achieves the best performance, outperforming all previous inference-time scaling approaches.