# Determinism of Randomness: Prompt-Residual Seed Shaping for Diffusion Generation

arXiv: https://arxiv.org/abs/2511.07756 · HTML: https://mlsanity.com/paper/2511.07756/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Image generation, text-to-image and editing, one of 14 directions in Diffusion models.
- Builds on 24 of its 29 references that are in the map.
- First posted on arXiv 11 Nov 2025.

## Placed in

- Diffusion models / [Image generation, text-to-image and editing](https://mlsanity.com/diffusion/image-generation-text-to-image-and-editing/)

## Builds on (most cited first, 24 of 24)

- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [DINOv2: Learning Robust Visual Features without Supervision](https://mlsanity.com/paper/2304.07193/) (2023)
- [Photorealistic Text-to-Image Diffusion Models with Deep Language Understanding](https://mlsanity.com/paper/2205.11487/) (2022)
- [Rethinking the Inception Architecture for Computer Vision](https://mlsanity.com/paper/1512.00567/) (2015)
- [SDXL: Improving Latent Diffusion Models for High-Resolution Image Synthesis](https://mlsanity.com/paper/2307.01952/) (2023)
- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
- [Wan: Open and Advanced Large-Scale Video Generative Models](https://mlsanity.com/paper/2503.20314/) (2025)
- [Stable Video Diffusion: Scaling Latent Video Diffusion Models to Large Datasets](https://mlsanity.com/paper/2311.15127/) (2023)
- [CLIPScore: A Reference-free Evaluation Metric for Image Captioning](https://mlsanity.com/paper/2104.08718/) (2021)
- [VBench: Comprehensive Benchmark Suite for Video Generative Models](https://mlsanity.com/paper/2311.17982/) (2023)
- [ImageReward: Learning and Evaluating Human Preferences for Text-to-Image Generation](https://mlsanity.com/paper/2304.05977/) (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)
- [Structured 3D Latents for Scalable and Versatile 3D Generation](https://mlsanity.com/paper/2412.01506/) (2024)
- [Evaluating Text-to-Visual Generation with Image-to-Text Generation](https://mlsanity.com/paper/2404.01291/) (2024)
- [Flow Matching on General Geometries](https://mlsanity.com/paper/2302.03660/) (2023)
- [Latent Space Oddity: on the Curvature of Deep Generative Models](https://mlsanity.com/paper/1710.11379/) (2017)
- [Dynamical Regimes of Diffusion Models](https://mlsanity.com/paper/2402.18491/) (2024)
- [InitNO: Boosting Text-to-Image Diffusion Models via Initial Noise Optimization](https://mlsanity.com/paper/2404.04650/) (2024)
- [Golden Noise for Diffusion Models: A Learning Framework](https://mlsanity.com/paper/2411.09502/) (2024)
- [Not All Noises Are Created Equally:Diffusion Noise Selection and Optimization](https://mlsanity.com/paper/2407.14041/) (2024)
- [Manifolds, Random Matrices and Spectral Gaps: The geometric phases of generative diffusion](https://mlsanity.com/paper/2410.05898/) (2024)
- [Scaling Riemannian Diffusion Models](https://mlsanity.com/paper/2310.20030/) (2023)
- [Advancing Diffusion Models: Alias-Free Resampling and Enhanced Rotational Equivariance](https://mlsanity.com/paper/2411.09174/) (2024)

## Abstract (arXiv)

Diffusion models start generation from an isotropic Gaussian latent, yet changing only the random seed can lead to large differences in prompt faithfulness, composition, and visual quality. We study this seed sensitivity through the semantic map from initial noise to generated meaning. Although the sampling flow is locally invertible, the subsequent semantic projection is many-to-one, inducing a degenerate pullback semi-metric on the latent space: most local directions are nearly semantic-invariant, while semantic-sensitive variation is concentrated in a much smaller horizontal subspace. This provides an explanatory geometric view of the seed lottery. Motivated by this view, we introduce a training-free prompt-residual seed-shaping procedure. Rather than claiming to recover the exact horizontal space, the method uses a single high-noise cold-start prompt residual as a model-coupled proxy, injects only its tangential component, and retracts the seed to the original Gaussian radius shell. This keeps the initialization prior-compatible while adding only one conditional/unconditional probe before standard sampling. Across multiple generation benchmarks, the method improves alignment and quality metrics over standard sampling, supporting both the practical value of the proxy and the explanatory relevance of semantic anisotropy.