# Couple to Control: Joint Initial Noise Design in Diffusion Models

arXiv: https://arxiv.org/abs/2605.11311 · HTML: https://mlsanity.com/paper/2605.11311/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 29 of its 39 references that are in the map.
- First posted on arXiv 11 May 2026.

## Placed in

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

## Builds on (most cited first, 29 of 29)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [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)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [SDEdit: Guided Image Synthesis and Editing with Stochastic Differential Equations](https://mlsanity.com/paper/2108.01073/) (2021)
- [LSUN: Construction of a Large-scale Image Dataset using Deep Learning with Humans in the Loop](https://mlsanity.com/paper/1506.03365/) (2015)
- [Pick-a-Pic: An Open Dataset of User Preferences for Text-to-Image Generation](https://mlsanity.com/paper/2305.01569/) (2023)
- [The Vendi Score: A Diversity Evaluation Metric for Machine Learning](https://mlsanity.com/paper/2210.02410/) (2022)
- [A Self-Supervised Descriptor for Image Copy Detection](https://mlsanity.com/paper/2202.10261/) (2022)
- [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)
- [Not All Noises Are Created Equally:Diffusion Noise Selection and Optimization](https://mlsanity.com/paper/2407.14041/) (2024)
- [DMPlug: A Plug-in Method for Solving Inverse Problems with Diffusion Models](https://mlsanity.com/paper/2405.16749/) (2024)
- [Inference-Time Alignment of Diffusion Models with Direct Noise Optimization](https://mlsanity.com/paper/2405.18881/) (2024)
- [Good Seed Makes a Good Crop: Discovering Secret Seeds in Text-to-Image Diffusion Models](https://mlsanity.com/paper/2405.14828/) (2024)
- [Blind Image Restoration via Fast Diffusion Inversion](https://mlsanity.com/paper/2405.19572/) (2024)
- [The Crystal Ball Hypothesis in diffusion models: Anticipating object positions from initial noise](https://mlsanity.com/paper/2406.01970/) (2024)
- [Estimating Convergence of Markov chains with L-Lag Couplings](https://mlsanity.com/paper/1905.09971/) (2019)
- [Diverse Text-to-Image Generation via Contrastive Noise Optimization](https://mlsanity.com/paper/2510.03813/) (2025)
- [On importance sampling and independent Metropolis-Hastings with an unbounded weight function](https://mlsanity.com/paper/2411.09514/) (2024)
- [Antithetic Noise in Diffusion Models](https://mlsanity.com/paper/2506.06185/) (2025)
- [Weak Diffusion Priors Can Still Achieve Strong Inverse-Problem Performance](https://mlsanity.com/paper/2601.22443/) (2026)
- [Unbiased Markov Chain Monte Carlo: what, why, and how](https://mlsanity.com/paper/2406.06851/) (2024)
- [CCS: Controllable and Constrained Sampling with Diffusion Models via Initial Noise Perturbation](https://mlsanity.com/paper/2502.04670/) (2025)
- [FMPlug: Plug-In Foundation Flow-Matching Priors for Inverse Problems](https://mlsanity.com/paper/2508.00721/) (2025)

## Built on by (most cited first, 2 of 2)

- [Making two action heads agree: coordination mechanisms and a runtime collapse certificate for flow-matching policies](https://mlsanity.com/paper/2608.15748/) (2026)
- [PAWBench: How Far Are We from Probabilistically Aligned World Modeling?](https://mlsanity.com/paper/2608.27345/) (2026)

## Abstract (arXiv)

Diffusion models typically generate image batches from independent Gaussian initial noises. We argue that this independence assumption is only one choice within a broader class of valid joint noise designs. Instead, one can specify a coupling of the initial noises: each noise remains marginally standard Gaussian, so the pretrained diffusion model receives the same single-sample input distribution, while the dependence across samples is chosen by design. This reframes initial-noise control from selecting or optimizing individual seeds to designing the dependence structure of a multi-sample gallery. This view gives a general framework for initial-noise design, covering several existing methods as special cases and leading naturally to new coupled-noise constructions. Coupled noise can improve generation on its own without adding sampling cost, and it is flexible enough to serve as a structured initialization for optimization-based pipelines when additional computation is available. Empirically, repulsive Gaussian coupling improves gallery diversity on SD1.5, SDXL, and SD3 while largely preserving prompt alignment and image quality. It matches or outperforms recent test-time noise-optimization baselines on several diversity metrics at the same sampling cost as independent generation. Subspace couplings also support fixed-object background generation, producing diverse, natural backgrounds compared with specialized inpainting baselines, with a tunable trade-off in foreground fidelity.