# Manifold-Constrained Noise Optimization for Diverse Diffusion Sampling

arXiv: https://arxiv.org/abs/2607.23937 · HTML: https://mlsanity.com/paper/2607.23937/

## 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 19 of its 26 references that are in the map.
- First posted on arXiv 27 Jul 2026.

## Placed in

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

## Builds on (most cited first, 19 of 19)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [DINOv2: Learning Robust Visual Features without Supervision](https://mlsanity.com/paper/2304.07193/) (2023)
- [CLIPScore: A Reference-free Evaluation Metric for Image Captioning](https://mlsanity.com/paper/2104.08718/) (2021)
- [Exploring CLIP for Assessing the Look and Feel of Images](https://mlsanity.com/paper/2207.12396/) (2022)
- [GenEval: An Object-Focused Framework for Evaluating Text-to-Image Alignment](https://mlsanity.com/paper/2310.11513/) (2023)
- [Improved Distribution Matching Distillation for Fast Image Synthesis](https://mlsanity.com/paper/2405.14867/) (2024)
- [ELLA: Equip Diffusion Models with LLM for Enhanced Semantic Alignment](https://mlsanity.com/paper/2403.05135/) (2024)
- [DreamSim: Learning New Dimensions of Human Visual Similarity using Synthetic Data](https://mlsanity.com/paper/2306.09344/) (2023)
- [The Vendi Score: A Diversity Evaluation Metric for Machine Learning](https://mlsanity.com/paper/2210.02410/) (2022)
- [CADS: Unleashing the Diversity of Diffusion Models through Condition-Annealed Sampling](https://mlsanity.com/paper/2310.17347/) (2023)
- [A Fourier Space Perspective on Diffusion Models](https://mlsanity.com/paper/2505.11278/) (2025)
- [Distilling Diversity and Control in Diffusion Models](https://mlsanity.com/paper/2503.10637/) (2025)
- [Diversity-Preserved Distribution Matching Distillation for Fast Visual Synthesis](https://mlsanity.com/paper/2602.03139/) (2026)
- [Scaling Group Inference for Diverse and High-Quality Generation](https://mlsanity.com/paper/2508.15773/) (2025)
- [Diverse Text-to-Image Generation via Contrastive Noise Optimization](https://mlsanity.com/paper/2510.03813/) (2025)
- [It's Never Too Late: Noise Optimization for Collapse Recovery in Trained Diffusion Models](https://mlsanity.com/paper/2601.00090/) (2025)
- [1.x-Distill: Breaking the Diversity, Quality, and Efficiency Barrier in Distribution Matching Distillation](https://mlsanity.com/paper/2604.04018/) (2026)
- [LENS: Low-Frequency Eigen Noise Shaping for Efficient Diffusion Sampling](https://mlsanity.com/paper/2605.07253/) (2026)

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

- [Manifold-Constrained Initial Noise Optimization for Efficient Generative Model Alignment](https://mlsanity.com/paper/2610.00365/) (2026)

## Abstract (arXiv)

Few-step distilled diffusion models generate high-quality images quickly, but often lose per-prompt diversity, producing near-identical samples across random seeds. Optimizing the initial noise at inference time offers an appealing way to recover this diversity, yet existing methods directly update the initial noise in an unconstrained Euclidean space, ignoring both the geometry of the Gaussian prior and the model's sensitivity to noise frequencies. They therefore introduce auxiliary quality-control objectives to maintain generation fidelity, adding compute and weighting hyperparameters while still requiring conservative updates to prevent degradation. In this work, we propose MoNO, a training-free method that performs Manifold-constrained Noise Optimization on a low-dimensional, quality-stabilizing noise manifold. MoNO sequentially optimizes each new initial noise so that its predicted visual feature complements previous generations, while Riemannian updates on an affine low-frequency sphere preserve prior likelihood and fix unstable high-frequency components by construction. This enables large geodesic steps, removes the need for auxiliary quality-control objectives, and converges in far fewer iterations than prior noise-optimization methods. Experiments with multiple distilled text-to-image diffusion models show that MoNO consistently improves per-prompt diversity while maintaining image quality.