# LENS: Low-Frequency Eigen Noise Shaping for Efficient Diffusion Sampling

arXiv: https://arxiv.org/abs/2605.07253 · HTML: https://mlsanity.com/paper/2605.07253/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 42 of its 46 references that are in the map.
- First posted on arXiv 8 May 2026.

## Placed in

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

## Builds on (most cited first, 30 of 42)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [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)
- [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)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [DINOv2: Learning Robust Visual Features without Supervision](https://mlsanity.com/paper/2304.07193/) (2023)
- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
- [CLIPScore: A Reference-free Evaluation Metric for Image Captioning](https://mlsanity.com/paper/2104.08718/) (2021)
- [Do ImageNet Classifiers Generalize to ImageNet?](https://mlsanity.com/paper/1902.10811/) (2019)
- [ImageReward: Learning and Evaluating Human Preferences for Text-to-Image Generation](https://mlsanity.com/paper/2304.05977/) (2023)
- [One-step Diffusion with Distribution Matching Distillation](https://mlsanity.com/paper/2311.18828/) (2023)
- [Pick-a-Pic: An Open Dataset of User Preferences for Text-to-Image Generation](https://mlsanity.com/paper/2305.01569/) (2023)
- [Human Preference Score v2: A Solid Benchmark for Evaluating Human Preferences of Text-to-Image Synthesis](https://mlsanity.com/paper/2306.09341/) (2023)
- [Adversarial Diffusion Distillation](https://mlsanity.com/paper/2311.17042/) (2023)
- [ELLA: Equip Diffusion Models with LLM for Enhanced Semantic Alignment](https://mlsanity.com/paper/2403.05135/) (2024)
- [Training-Free Structured Diffusion Guidance for Compositional Text-to-Image Synthesis](https://mlsanity.com/paper/2212.05032/) (2022)
- [Text-to-image Diffusion Models in Generative AI: A Survey](https://mlsanity.com/paper/2303.07909/) (2023)
- [Hyper-SD: Trajectory Segmented Consistency Model for Efficient Image Synthesis](https://mlsanity.com/paper/2404.13686/) (2024)
- [InitNO: Boosting Text-to-Image Diffusion Models via Initial Noise Optimization](https://mlsanity.com/paper/2404.04650/) (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)
- [End-to-End Diffusion Latent Optimization Improves Classifier Guidance](https://mlsanity.com/paper/2303.13703/) (2023)
- [Optimizing Diffusion Noise Can Serve As Universal Motion Priors](https://mlsanity.com/paper/2312.11994/) (2023)
- [Golden Noise for Diffusion Models: A Learning Framework](https://mlsanity.com/paper/2411.09502/) (2024)
- [Inference-Time Alignment in Diffusion Models with Reward-Guided Generation: Tutorial and Review](https://mlsanity.com/paper/2501.09685/) (2025)
- [SANA-Sprint: One-Step Diffusion with Continuous-Time Consistency Distillation](https://mlsanity.com/paper/2503.09641/) (2025)
- [DITTO: Diffusion Inference-Time T-Optimization for Music Generation](https://mlsanity.com/paper/2401.12179/) (2024)
- [EM Distillation for One-step Diffusion Models](https://mlsanity.com/paper/2405.16852/) (2024)
- [GenEval 2: Addressing Benchmark Drift in Text-to-Image Evaluation](https://mlsanity.com/paper/2512.16853/) (2025)

## Built on by (most cited first, 1 of 1)

- [Manifold-Constrained Noise Optimization for Diverse Diffusion Sampling](https://mlsanity.com/paper/2607.23937/) (2026)

## Abstract (arXiv)

Distilled diffusion models accelerate image generation by reducing the number of denoising steps, but often suffer from degraded image quality. To mitigate this trade-off, test-time optimization methods improve quality, yet their iterative nature incurs substantial computational overhead and leads to slow inference, limiting practical usability. Recent hypernetwork-based approaches amortize this process during training, but still require costly noise modulation in high-dimensional latent spaces. In this work, we propose LENS (Low-frequency Eigen Noise Shaping), an efficient noise modulation framework that operates in a low-dimensional subspace. Our approach is motivated by the observation that low-frequency components of the noise largely determine the global structure and visual fidelity of generated images. Based on this observation, we provide a theoretical justification for restricting modulation to the low-frequency subspace and derive a principled training objective. Building on this, LENS employs a lightweight, standalone network to selectively modulate these components, enabling efficient and targeted noise modulation. Extensive experiments demonstrate that LENS achieves competitive image quality while reducing FLOPs by 400-700×, model parameters by 25-75×, and inference-time overhead by 10-20× compared to prior methods.