# A General Framework for Inference-time Scaling and Steering of Diffusion Models

arXiv: https://arxiv.org/abs/2501.06848 · HTML: https://mlsanity.com/paper/2501.06848/

## Key facts

- Cited by 224 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 29 of its 69 references that are in the map.
- First posted on arXiv 12 Jan 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, 29 of 29)

- [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)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [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)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [GLIDE: Towards Photorealistic Image Generation and Editing with Text-Guided Diffusion Models](https://mlsanity.com/paper/2112.10741/) (2021)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [Variational Diffusion Models](https://mlsanity.com/paper/2107.00630/) (2021)
- [Diffusion-LM Improves Controllable Text Generation](https://mlsanity.com/paper/2205.14217/) (2022)
- [Training Diffusion Models with Reinforcement Learning](https://mlsanity.com/paper/2305.13301/) (2023)
- [Neural Network Acceptability Judgments](https://mlsanity.com/paper/1805.12471/) (2018)
- [Human Preference Score v2: A Solid Benchmark for Evaluating Human Preferences of Text-to-Image Synthesis](https://mlsanity.com/paper/2306.09341/) (2023)
- [Simplified and Generalized Masked Diffusion for Discrete Data](https://mlsanity.com/paper/2406.04329/) (2024)
- [DiffuSeq: Sequence to Sequence Text Generation with Diffusion Models](https://mlsanity.com/paper/2210.08933/) (2022)
- [Diffusion probabilistic modeling of protein backbones in 3D for the motif-scaffolding problem](https://mlsanity.com/paper/2206.04119/) (2022)
- [Adjoint Matching: Fine-tuning Flow and Diffusion Generative Models with Memoryless Stochastic Optimal Control](https://mlsanity.com/paper/2409.08861/) (2024)
- [SSD-LM: Semi-autoregressive Simplex-based Diffusion Language Model for Text Generation and Modular Control](https://mlsanity.com/paper/2210.17432/) (2022)
- [Protein Design with Guided Discrete Diffusion](https://mlsanity.com/paper/2305.20009/) (2023)
- [Infini-gram: Scaling Unbounded n-gram Language Models to a Trillion Tokens](https://mlsanity.com/paper/2401.17377/) (2024)
- [Likelihood-Based Diffusion Language Models](https://mlsanity.com/paper/2305.18619/) (2023)
- [Derivative-Free Guidance in Continuous and Discrete Diffusion Models with Soft Value-Based Decoding](https://mlsanity.com/paper/2408.08252/) (2024)
- [RL with KL penalties is better viewed as Bayesian inference](https://mlsanity.com/paper/2205.11275/) (2022)
- [Probabilistic Inference in Language Models via Twisted Sequential Monte Carlo](https://mlsanity.com/paper/2404.17546/) (2024)
- [Sequential Monte Carlo Steering of Large Language Models using Probabilistic Programs](https://mlsanity.com/paper/2306.03081/) (2023)
- [Monte Carlo guided Diffusion for Bayesian linear inverse problems](https://mlsanity.com/paper/2308.07983/) (2023)
- [Conditional sampling within generative diffusion models](https://mlsanity.com/paper/2409.09650/) (2024)
- [ParaGuide: Guided Diffusion Paraphrasers for Plug-and-Play Textual Style Transfer](https://mlsanity.com/paper/2308.15459/) (2023)

## Built on by (most cited first, 30 of 224)

- [SANA 1.5: Efficient Scaling of Training-Time and Inference-Time Compute in Linear Diffusion Transformer](https://mlsanity.com/paper/2501.18427/) (2025)
- [Feynman-Kac Correctors in Diffusion: Annealing, Guidance, and Product of Experts](https://mlsanity.com/paper/2503.02819/) (2025)
- [Inference-Time Alignment in Diffusion Models with Reward-Guided Generation: Tutorial and Review](https://mlsanity.com/paper/2501.09685/) (2025)
- [From Reflection to Perfection: Scaling Inference-Time Optimization for Text-to-Image Diffusion Models via Reflection Tuning](https://mlsanity.com/paper/2504.16080/) (2025)
- [Inference-time Scaling of Diffusion Models through Classical Search](https://mlsanity.com/paper/2505.23614/) (2025)
- [Fast Solvers for Discrete Diffusion Models: Theory and Applications of High-Order Algorithms](https://mlsanity.com/paper/2502.00234/) (2025)
- [Categorical Flow Maps](https://mlsanity.com/paper/2602.12233/) (2026)
- [Reflect-DiT: Inference-Time Scaling for Text-to-Image Diffusion Transformers via In-Context Reflection](https://mlsanity.com/paper/2503.12271/) (2025)
- [Inference-Time Text-to-Video Alignment with Diffusion Latent Beam Search](https://mlsanity.com/paper/2501.19252/) (2025)
- [Scaling Image and Video Generation via Test-Time Evolutionary Search](https://mlsanity.com/paper/2505.17618/) (2025)
- [Fine-Tuning Discrete Diffusion Models with Policy Gradient Methods](https://mlsanity.com/paper/2502.01384/) (2025)
- [Dynamic Search for Inference-Time Alignment in Diffusion Models](https://mlsanity.com/paper/2503.02039/) (2025)
- [Inference-time Physics Alignment of Video Generative Models with Latent World Models](https://mlsanity.com/paper/2601.10553/) (2026)
- [Q-learning with Adjoint Matching](https://mlsanity.com/paper/2601.14234/) (2026)
- [Meta Flow Maps enable scalable reward alignment](https://mlsanity.com/paper/2601.14430/) (2026)
- [Diffusion Tree Sampling: Scalable inference-time alignment of diffusion models](https://mlsanity.com/paper/2506.20701/) (2025)
- [Energy-Based Transformers are Scalable Learners and Thinkers](https://mlsanity.com/paper/2507.02092/) (2025)
- [Diamond Maps: Efficient Reward Alignment via Stochastic Flow Maps](https://mlsanity.com/paper/2602.05993/) (2026)
- [Discrete Flow Maps](https://mlsanity.com/paper/2604.09784/) (2026)
- [Scaling Offline RL via Efficient and Expressive Shortcut Models](https://mlsanity.com/paper/2505.22866/) (2025)
- [d2: Improving Reasoning in Diffusion Language Models via Trajectory Likelihood Estimation](https://mlsanity.com/paper/2509.21474/) (2025)
- [Target Concrete Score Matching: A Holistic Framework for Discrete Diffusion](https://mlsanity.com/paper/2504.16431/) (2025)
- [Training-Free Guidance Beyond Differentiability: Scalable Path Steering with Tree Search in Diffusion and Flow Models](https://mlsanity.com/paper/2502.11420/) (2025)
- [DriftLite: Lightweight Drift Control for Inference-Time Scaling of Diffusion Models](https://mlsanity.com/paper/2509.21655/) (2025)
- [Structuring The Future: Diffusion LLM Speculative Decoding via Calibrated Draft Graphs](https://mlsanity.com/paper/2509.18085/) (2025)
- [Composition and Control with Distilled Energy Diffusion Models and Sequential Monte Carlo](https://mlsanity.com/paper/2502.12786/) (2025)
- [A Survey of Slow Thinking-based Reasoning LLMs using Reinforced Learning and Inference-time Scaling Law](https://mlsanity.com/paper/2505.02665/) (2025)
- [Split Gibbs Discrete Diffusion Posterior Sampling](https://mlsanity.com/paper/2503.01161/) (2025)
- [RNE: plug-and-play diffusion inference-time control and energy-based training](https://mlsanity.com/paper/2506.05668/) (2025)
- [GLASS Flows: Transition Sampling for Alignment of Flow and Diffusion Models](https://mlsanity.com/paper/2509.25170/) (2025)

## Abstract (arXiv)

Diffusion models produce impressive results in modalities ranging from images and video to protein design and text. However, generating samples with user-specified properties remains a challenge. Recent research proposes fine-tuning models to maximize rewards that capture desired properties, but these methods require expensive training and are prone to mode collapse. In this work, we present Feynman-Kac (FK) steering, an inference-time framework for steering diffusion models with reward functions. FK steering works by sampling a system of multiple interacting diffusion processes, called particles, and resampling particles at intermediate steps based on scores computed using functions called potentials. Potentials are defined using rewards for intermediate states and are selected such that a high value indicates that the particle will yield a high-reward sample. We explore various choices of potentials, intermediate rewards, and samplers. We evaluate FK steering on text-to-image and text diffusion models. For steering text-to-image models with a human preference reward, we find that FK steering a 0.8B parameter model outperforms a 2.6B parameter fine-tuned model on prompt fidelity, with faster sampling and no training. For steering text diffusion models with rewards for text quality and specific text attributes, we find that FK steering generates lower perplexity, more linguistically acceptable outputs and enables gradient-free control of attributes like toxicity. Our results demonstrate that inference-time scaling and steering of diffusion models - even with off-the-shelf rewards - can provide significant sample quality gains and controllability benefits. Code is available at https://github.com/zacharyhorvitz/Fk-Diffusion-Steering .