# Noise Hypernetworks: Amortizing Test-Time Compute in Diffusion Models

arXiv: https://arxiv.org/abs/2508.09968 · HTML: https://mlsanity.com/paper/2508.09968/

## Key facts

- Cited by 35 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 100 of its 108 references that are in the map.
- First posted on arXiv 13 Aug 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 100)

- [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)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [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)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [DINOv2: Learning Robust Visual Features without Supervision](https://mlsanity.com/paper/2304.07193/) (2023)
- [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)
- [BLIP: Bootstrapping Language-Image Pre-training for Unified Vision-Language Understanding and Generation](https://mlsanity.com/paper/2201.12086/) (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)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (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)
- [s1: Simple test-time scaling](https://mlsanity.com/paper/2501.19393/) (2025)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Variational Diffusion Models](https://mlsanity.com/paper/2107.00630/) (2021)
- [Tulu 3: Pushing Frontiers in Open Language Model Post-Training](https://mlsanity.com/paper/2411.15124/) (2024)
- [ImageReward: Learning and Evaluating Human Preferences for Text-to-Image Generation](https://mlsanity.com/paper/2304.05977/) (2023)
- [HyperNetworks](https://mlsanity.com/paper/1609.09106/) (2016)
- [Building Normalizing Flows with Stochastic Interpolants](https://mlsanity.com/paper/2209.15571/) (2022)
- [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)
- [GenEval: An Object-Focused Framework for Evaluating Text-to-Image Alignment](https://mlsanity.com/paper/2310.11513/) (2023)
- [Human Preference Score v2: A Solid Benchmark for Evaluating Human Preferences of Text-to-Image Synthesis](https://mlsanity.com/paper/2306.09341/) (2023)
- [Latent Consistency Models: Synthesizing High-Resolution Images with Few-Step Inference](https://mlsanity.com/paper/2310.04378/) (2023)

## Built on by (most cited first, 30 of 35)

- [Distribution Matching Distillation Meets Reinforcement Learning](https://mlsanity.com/paper/2511.13649/) (2025)
- [Diamond Maps: Efficient Reward Alignment via Stochastic Flow Maps](https://mlsanity.com/paper/2602.05993/) (2026)
- [Pathwise Test-Time Correction for Autoregressive Long Video Generation](https://mlsanity.com/paper/2602.05871/) (2026)
- [SuperFlow: Training Flow Matching Models with RL on the Fly](https://mlsanity.com/paper/2512.17951/) (2025)
- [Fine-Tuning Diffusion Models via Intermediate Distribution Shaping](https://mlsanity.com/paper/2510.02692/) (2025)
- [AutoRefiner: Improving Autoregressive Video Diffusion Models via Reflective Refinement Over the Stochastic Sampling Path](https://mlsanity.com/paper/2512.11203/) (2025)
- [HyperAlign: Hypernetwork for Efficient Test-Time Alignment of Diffusion Models](https://mlsanity.com/paper/2601.15968/) (2026)
- [ReFORM: Reflected Flows for On-support Offline RL via Noise Manipulation](https://mlsanity.com/paper/2602.05051/) (2026)
- [FASTER: Value-Guided Sampling for Fast RL](https://mlsanity.com/paper/2604.19730/) (2026)
- [Lagrangian Perturbation Diffusion Steering: Latent Reinforcement Learning for Generative Policies](https://mlsanity.com/paper/2606.01151/) (2026)
- [Stitch: Training-Free Position Control in Multimodal Diffusion Transformers](https://mlsanity.com/paper/2509.26644/) (2025)
- [Noise-Level Diffusion Guidance: Well Begun is Half Done](https://mlsanity.com/paper/2509.13936/) (2025)
- [TAUE: Training-free Noise Transplant and Cultivation Diffusion Model](https://mlsanity.com/paper/2511.02580/) (2025)
- [Gradient Preconditioning for Efficient and Reliable Reward-Guided Generation](https://mlsanity.com/paper/2602.08646/) (2026)
- [S3: Stratified Scaling Search for Test-Time in Diffusion Language Models](https://mlsanity.com/paper/2604.06260/) (2026)
- [MIRO: MultI-Reward cOnditioned pretraining improves T2I quality and efficiency](https://mlsanity.com/paper/2510.25897/) (2025)
- [Rethinking Test Time Scaling for Flow-Matching Generative Models](https://mlsanity.com/paper/2511.22242/) (2025)
- [LGTM: Training-Free Light-Guided Text-to-Image Diffusion Model via Initial Noise Manipulation](https://mlsanity.com/paper/2603.24086/) (2026)
- [LENS: Low-Frequency Eigen Noise Shaping for Efficient Diffusion Sampling](https://mlsanity.com/paper/2605.07253/) (2026)
- [StressDream: Steering Video World Models for Robust Policy Evaluation and Improvement](https://mlsanity.com/paper/2606.00267/) (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)
- [Diffusion Fine-tuning with Rewarded Moment Matching Distillation](https://mlsanity.com/paper/2606.30414/) (2026)
- [Retrieving and Refining Winning Noise Tickets for Diffusion-Based Motion Generation](https://mlsanity.com/paper/2607.06843/) (2026)
- [World-Coherent Decoding: Self-Verifying Test-Time Planning for World Action Models](https://mlsanity.com/paper/2609.02159/) (2026)
- [ReconPlusGen: Injecting Reconstruction Prior into Multi-view 3D Generation through Noise Inversion and Modulation](https://mlsanity.com/paper/2609.11129/) (2026)
- [FluxLite: Inference-Time Proposal Control for Discrete Diffusion Models](https://mlsanity.com/paper/2609.35947/) (2026)
- [Rethinking Refinement: Correcting Generative Bias without Noise Injection](https://mlsanity.com/paper/2601.21182/) (2026)
- [Rethinking Global Text Conditioning in Diffusion Transformers](https://mlsanity.com/paper/2602.09268/) (2026)
- [Does Semantic Noise Initialization Transfer from Images to Videos? A Paired Diagnostic Study](https://mlsanity.com/paper/2603.06672/) (2026)
- [The Latent Color Subspace: Emergent Order in High-Dimensional Chaos](https://mlsanity.com/paper/2603.12261/) (2026)

## Abstract (arXiv)

The new paradigm of test-time scaling has yielded remarkable breakthroughs in Large Language Models (LLMs) (e.g. reasoning models) and in generative vision models, allowing models to allocate additional computation during inference to effectively tackle increasingly complex problems. Despite the improvements of this approach, an important limitation emerges: the substantial increase in computation time makes the process slow and impractical for many applications. Given the success of this paradigm and its growing usage, we seek to preserve its benefits while eschewing the inference overhead. In this work we propose one solution to the critical problem of integrating test-time scaling knowledge into a model during post-training. Specifically, we replace reward guided test-time noise optimization in diffusion models with a Noise Hypernetwork that modulates initial input noise. We propose a theoretically grounded framework for learning this reward-tilted distribution for distilled generators, through a tractable noise-space objective that maintains fidelity to the base model while optimizing for desired characteristics. We show that our approach recovers a substantial portion of the quality gains from explicit test-time optimization at a fraction of the computational cost. Code is available at https://github.com/ExplainableML/HyperNoise