# Test-Time Scaling of Diffusion Models via Noise Trajectory Search

arXiv: https://arxiv.org/abs/2506.03164 · HTML: https://mlsanity.com/paper/2506.03164/

## Key facts

- Cited by 30 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 32 of its 42 references that are in the map.
- First posted on arXiv 24 May 2025.

## Placed in

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

## Builds on (most cited first, 30 of 32)

- [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)
- [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)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Emerging Properties in Self-Supervised Vision Transformers](https://mlsanity.com/paper/2104.14294/) (2021)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [SDXL: Improving Latent Diffusion Models for High-Resolution Image Synthesis](https://mlsanity.com/paper/2307.01952/) (2023)
- [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (2023)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016)
- [s1: Simple test-time scaling](https://mlsanity.com/paper/2501.19393/) (2025)
- [ImageReward: Learning and Evaluating Human Preferences for Text-to-Image Generation](https://mlsanity.com/paper/2304.05977/) (2023)
- [Large Language Diffusion Models](https://mlsanity.com/paper/2502.09992/) (2025)
- [Diffusion Model Alignment Using Direct Preference Optimization](https://mlsanity.com/paper/2311.12908/) (2023)
- [Universal Guidance for Diffusion Models](https://mlsanity.com/paper/2302.07121/) (2023)
- [InstaFlow: One Step is Enough for High-Quality Diffusion-Based Text-to-Image Generation](https://mlsanity.com/paper/2309.06380/) (2023)
- [Inference-Time Scaling for Diffusion Models beyond Scaling Denoising Steps](https://mlsanity.com/paper/2501.09732/) (2025)
- [Adjoint Matching: Fine-tuning Flow and Diffusion Generative Models with Memoryless Stochastic Optimal Control](https://mlsanity.com/paper/2409.08861/) (2024)
- [Restart Sampling for Improving Generative Processes](https://mlsanity.com/paper/2306.14878/) (2023)
- [Not All Noises Are Created Equally:Diffusion Noise Selection and Optimization](https://mlsanity.com/paper/2407.14041/) (2024)
- [Inference-Time Alignment of Diffusion Models with Direct Noise Optimization](https://mlsanity.com/paper/2405.18881/) (2024)
- [A Noise is Worth Diffusion Guidance](https://mlsanity.com/paper/2412.03895/) (2024)
- [Improved Noise Schedule for Diffusion Training](https://mlsanity.com/paper/2407.03297/) (2024)
- [Inference-Time Scaling for Flow Models via Stochastic Generation and Rollover Budget Forcing](https://mlsanity.com/paper/2503.19385/) (2025)
- [Training-free Diffusion Model Alignment with Sampling Demons](https://mlsanity.com/paper/2410.05760/) (2024)
- [Confronting Reward Overoptimization for Diffusion Models: A Perspective of Inductive and Primacy Biases](https://mlsanity.com/paper/2402.08552/) (2024)
- [A Closer Look at Time Steps is Worthy of Triple Speed-Up for Diffusion Model Training](https://mlsanity.com/paper/2405.17403/) (2024)

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

- [Attention Is All You Need for KV Cache in Diffusion LLMs](https://mlsanity.com/paper/2510.14973/) (2025)
- [Test-time scaling of diffusions with flow maps](https://mlsanity.com/paper/2511.22688/) (2025)
- [Scaling Atomistic Protein Binder Design with Generative Pretraining and Test-Time Compute](https://mlsanity.com/paper/2603.27950/) (2026)
- [Inference-Time Scaling of Discrete Diffusion Models via Importance Weighting and Optimal Proposal Design](https://mlsanity.com/paper/2505.22524/) (2025)
- [SuperFlow: Training Flow Matching Models with RL on the Fly](https://mlsanity.com/paper/2512.17951/) (2025)
- [From Scale to Speed: Adaptive Test-Time Scaling for Image Editing](https://mlsanity.com/paper/2603.00141/) (2026)
- [Scale Where It Matters: Training-Free Localized Scaling for Diffusion Models](https://mlsanity.com/paper/2511.19917/) (2025)
- [Contrastive Distribution Matching for Amortized Sequential Monte Carlo in Discrete Diffusion](https://mlsanity.com/paper/2605.23346/) (2026)
- [HyperAlign: Hypernetwork for Efficient Test-Time Alignment of Diffusion Models](https://mlsanity.com/paper/2601.15968/) (2026)
- [Stream-T1: Test-Time Scaling for Streaming Video Generation](https://mlsanity.com/paper/2605.04461/) (2026)
- [Entropy Aware Reward Guidance for Diffusion Language Model Alignment](https://mlsanity.com/paper/2602.05000/) (2026)
- [Tree Reward-Aligned Search for TReASURe in Masked Diffusion Language Models](https://mlsanity.com/paper/2509.23146/) (2025)
- [Guided Trajectory Optimization with Sparse Scaling for Test-Time Diffusion](https://mlsanity.com/paper/2605.21907/) (2026)
- [A2D2: Fine-Tuning Any-Length Discrete Diffusion for Adaptive Decoding](https://mlsanity.com/paper/2606.13565/) (2026)
- [Ctrl-Z Sampling: Scaling Diffusion Sampling with Controlled Random Zigzag Explorations](https://mlsanity.com/paper/2506.20294/) (2025)
- [Inference-Time Scaling of Diffusion Models for Infrared Data Generation](https://mlsanity.com/paper/2511.07362/) (2025)
- [Rethinking Test Time Scaling for Flow-Matching Generative Models](https://mlsanity.com/paper/2511.22242/) (2025)
- [ITS3D: Inference-Time Scaling for Text-Guided 3D Diffusion Models](https://mlsanity.com/paper/2511.22456/) (2025)
- [Can I Have Your Order? Monte-Carlo Tree Search for Slot Filling Ordering in Diffusion Language Models](https://mlsanity.com/paper/2602.12586/) (2026)
- [Early Failure Detection and Intervention in Video Diffusion Models](https://mlsanity.com/paper/2603.14320/) (2026)
- [SpecLoR: Spectral Lookahead Rectification for Motion-Coherent Text-to-Video Generation](https://mlsanity.com/paper/2606.11969/) (2026)
- [NoiseTilt: Noise-Tilted Reverse Kernels for Diffusion Reward Alignment](https://mlsanity.com/paper/2606.18066/) (2026)
- [FluxLite: Inference-Time Proposal Control for Discrete Diffusion Models](https://mlsanity.com/paper/2609.35947/) (2026)
- [Feature Space Analysis by Guided Diffusion Model](https://mlsanity.com/paper/2509.07936/) (2025)
- [Test-Time Alignment of Text-to-Image Diffusion Models via Null-Text Embedding Optimisation](https://mlsanity.com/paper/2511.20889/) (2025)
- [Test-Time Scaling in Multimodal Foundation Models: A Comprehensive Survey of Generation and Reasoning](https://mlsanity.com/paper/2606.08231/) (2026)
- [On the Design Space of Discrete Diffusion Online Adaptation for Molecular Optimization](https://mlsanity.com/paper/2607.02834/) (2026)
- [RRFC: Recursive Refinement via Feedback Conditioning for Iterative Image-to-Image Generation](https://mlsanity.com/paper/2608.15694/) (2026)
- [Leveraging Inference-Time Compute for Diffusion Models via Global Scheduling of Denoising Trajectories](https://mlsanity.com/paper/2609.22867/) (2026)
- [PreviewDiff: Multimodal Critic-Guided Search over Diffusion Latents](https://mlsanity.com/paper/2609.36199/) (2026)

## Abstract (arXiv)

The iterative and stochastic nature of diffusion models enables test-time scaling, whereby spending additional compute during denoising generates higher-fidelity samples. Increasing the number of denoising steps is the primary scaling axis, but this yields quickly diminishing returns. Instead optimizing the noise trajectory--the sequence of injected noise vectors--is promising, as the specific noise realizations critically affect sample quality; but this is challenging due to a high-dimensional search space, complex noise-outcome interactions, and costly trajectory evaluations. We address this by first casting diffusion as a Markov Decision Process (MDP) with a terminal reward, showing tree-search methods such as Monte Carlo tree search (MCTS) to be meaningful but impractical. To balance performance and efficiency, we then resort to a relaxation of MDP, where we view denoising as a sequence of independent contextual bandits. This allows us to introduce an ε-greedy search algorithm that globally explores at extreme timesteps and locally exploits during the intermediate steps where de-mixing occurs. Experiments on EDM and Stable Diffusion reveal state-of-the-art scores for class-conditioned/text-to-image generation, exceeding baselines by up to 164% and matching/exceeding MCTS performance. To our knowledge, this is the first practical method for test-time noise trajectory optimization of arbitrary (non-differentiable) rewards.