# Inference-Time Scaling for Diffusion Models beyond Scaling Denoising Steps

arXiv: https://arxiv.org/abs/2501.09732 · HTML: https://mlsanity.com/paper/2501.09732/

## Key facts

- Cited by 234 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 45 of its 99 references that are in the map.
- First posted on arXiv 16 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, 30 of 45)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [DINOv2: Learning Robust Visual Features without Supervision](https://mlsanity.com/paper/2304.07193/) (2023)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [CLIPScore: A Reference-free Evaluation Metric for Image Captioning](https://mlsanity.com/paper/2104.08718/) (2021)
- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://mlsanity.com/paper/2408.03314/) (2024)
- [Consistency Models](https://mlsanity.com/paper/2303.01469/) (2023)
- [An overview of gradient descent optimization algorithms](https://mlsanity.com/paper/1609.04747/) (2016)
- [Large Language Monkeys: Scaling Inference Compute with Repeated Sampling](https://mlsanity.com/paper/2407.21787/) (2024)
- [Training Diffusion Models with Reinforcement Learning](https://mlsanity.com/paper/2305.13301/) (2023)
- [Math-Shepherd: Verify and Reinforce LLMs Step-by-step without Human Annotations](https://mlsanity.com/paper/2312.08935/) (2023)
- [Gemini: A Family of Highly Capable Multimodal Models](https://mlsanity.com/paper/2312.11805/) (2023)
- [Training Deep Nets with Sublinear Memory Cost](https://mlsanity.com/paper/1604.06174/) (2016)
- [SiT: Exploring Flow and Diffusion-based Generative Models with Scalable Interpolant Transformers](https://mlsanity.com/paper/2401.08740/) (2024)
- [Movie Gen: A Cast of Media Foundation Models](https://mlsanity.com/paper/2410.13720/) (2024)
- [PixArt-Sigma: Weak-to-Strong Training of Diffusion Transformer for 4K Text-to-Image Generation](https://mlsanity.com/paper/2403.04692/) (2024)
- [The Effects of Reward Misspecification: Mapping and Mitigating Misaligned Models](https://mlsanity.com/paper/2201.03544/) (2022)
- [Inference Scaling Laws: An Empirical Analysis of Compute-Optimal Inference for Problem-Solving with Language Models](https://mlsanity.com/paper/2408.00724/) (2024)
- [Monte Carlo Tree Search Boosts Reasoning via Iterative Preference Learning](https://mlsanity.com/paper/2405.00451/) (2024)
- [Adjoint Matching: Fine-tuning Flow and Diffusion Generative Models with Memoryless Stochastic Optimal Control](https://mlsanity.com/paper/2409.08861/) (2024)
- [Stream of Search (SoS): Learning to Search in Language](https://mlsanity.com/paper/2404.03683/) (2024)
- [D-Flow: Differentiating through Flows for Controlled Generation](https://mlsanity.com/paper/2402.14017/) (2024)
- [ReNO: Enhancing One-step Text-to-Image Models through Reward-based Noise Optimization](https://mlsanity.com/paper/2406.04312/) (2024)
- [Golden Noise for Diffusion Models: A Learning Framework](https://mlsanity.com/paper/2411.09502/) (2024)

## Built on by (most cited first, 30 of 234)

- [Towards Reasoning Era: A Survey of Long Chain-of-Thought for Reasoning Large Language Models](https://mlsanity.com/paper/2503.09567/) (2025)
- [A Survey on Test-Time Scaling in Large Language Models: What, How, Where, and How Well?](https://mlsanity.com/paper/2503.24235/) (2025)
- [In-Context Edit: Enabling Instructional Image Editing with In-Context Generation in Large Scale Diffusion Transformer](https://mlsanity.com/paper/2504.20690/) (2025)
- [Remasking Discrete Diffusion Models with Inference-Time Scaling](https://mlsanity.com/paper/2503.00307/) (2025)
- [A Survey of Reinforcement Learning for Large Reasoning Models](https://mlsanity.com/paper/2509.08827/) (2025)
- [CoT-Valve: Length-Compressible Chain-of-Thought Tuning](https://mlsanity.com/paper/2502.09601/) (2025)
- [SANA 1.5: Efficient Scaling of Training-Time and Inference-Time Compute in Linear Diffusion Transformer](https://mlsanity.com/paper/2501.18427/) (2025)
- [Open-Sora 2.0: Training a Commercial-Level Video Generation Model in 200k](https://mlsanity.com/paper/2503.09642/) (2025)
- [Lumina-Image 2.0: A Unified and Efficient Image Generative Framework](https://mlsanity.com/paper/2503.21758/) (2025)
- [Llasa: Scaling Train-Time and Inference-Time Compute for Llama-based Speech Synthesis](https://mlsanity.com/paper/2502.04128/) (2025)
- [RewardDance: Reward Scaling in Visual Generation](https://mlsanity.com/paper/2509.08826/) (2025)
- [Inner Thinking Transformer: Leveraging Dynamic Depth Scaling to Foster Adaptive Internal Thinking](https://mlsanity.com/paper/2502.13842/) (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)
- [Scaling Text-to-Image Diffusion Transformers with Representation Autoencoders](https://mlsanity.com/paper/2601.16208/) (2026)
- [Inference-time Scaling of Diffusion Models through Classical Search](https://mlsanity.com/paper/2505.23614/) (2025)
- [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)
- [Video-T1: Test-Time Scaling for Video Generation](https://mlsanity.com/paper/2503.18942/) (2025)
- [RLVR-World: Training World Models with Reinforcement Learning](https://mlsanity.com/paper/2505.13934/) (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)
- [Inference-Time Scaling for Flow Models via Stochastic Generation and Rollover Budget Forcing](https://mlsanity.com/paper/2503.19385/) (2025)
- [Dynamic Search for Inference-Time Alignment in Diffusion Models](https://mlsanity.com/paper/2503.02039/) (2025)
- [Lumina-mGPT 2.0: Stand-Alone AutoRegressive Image Modeling](https://mlsanity.com/paper/2507.17801/) (2025)
- [Inference-time Physics Alignment of Video Generative Models with Latent World Models](https://mlsanity.com/paper/2601.10553/) (2026)
- [Meta Flow Maps enable scalable reward alignment](https://mlsanity.com/paper/2601.14430/) (2026)
- [Noise Hypernetworks: Amortizing Test-Time Compute in Diffusion Models](https://mlsanity.com/paper/2508.09968/) (2025)
- [Diffusion Tree Sampling: Scalable inference-time alignment of diffusion models](https://mlsanity.com/paper/2506.20701/) (2025)
- [U-REPA: Aligning Diffusion U-Nets to ViTs](https://mlsanity.com/paper/2503.18414/) (2025)
- [Energy-Based Transformers are Scalable Learners and Thinkers](https://mlsanity.com/paper/2507.02092/) (2025)

## Abstract (arXiv)

Generative models have made significant impacts across various domains, largely due to their ability to scale during training by increasing data, computational resources, and model size, a phenomenon characterized by the scaling laws. Recent research has begun to explore inference-time scaling behavior in Large Language Models (LLMs), revealing how performance can further improve with additional computation during inference. Unlike LLMs, diffusion models inherently possess the flexibility to adjust inference-time computation via the number of denoising steps, although the performance gains typically flatten after a few dozen. In this work, we explore the inference-time scaling behavior of diffusion models beyond increasing denoising steps and investigate how the generation performance can further improve with increased computation. Specifically, we consider a search problem aimed at identifying better noises for the diffusion sampling process. We structure the design space along two axes: the verifiers used to provide feedback, and the algorithms used to find better noise candidates. Through extensive experiments on class-conditioned and text-conditioned image generation benchmarks, our findings reveal that increasing inference-time compute leads to substantial improvements in the quality of samples generated by diffusion models, and with the complicated nature of images, combinations of the components in the framework can be specifically chosen to conform with different application scenario.