Couple to Control: Joint Initial Noise Design in Diffusion Models

Diffusion models typically generate batches from independent Gaussian initial noises. We argue that independence is only one choice within a broader class of valid joint noise designs. One can instead specify a coupling: each noise remains marginally standard Gaussian, while the dependence across samples is chosen by design. This reframes initial-noise control from selecting individual seeds to designing a multi-sample gallery's joint distribution. The framework covers familiar constructions and supports direct sampling, structured initialization for noise optimization, and amortized learning of couplings. Repulsive Gaussian coupling improves gallery diversity on SD1.5, SDXL, SD3, Qwen-Image, and FLUX.1-schnell with negligible initialization overhead. On its own, it matches or outperforms several recent test-time approaches for diverse generation on several diversity metrics at lower computational cost. Because it modifies only the initial noise, it can also be layered on top of contrastive noise optimization, particle guidance, and condition-annealed sampling to further improve pixel and perceptual diversity. We further extend the same design principle to video generation, where whole-latent coupling also yields significant gains in cross-video visual diversity. Code is available at https://anonymous.4open.science/r/diffusion-coupling-CE03/.