EvoSearch develops different mutation operations for initial noises and intermediate denoising states:
Initial noise mutation: The following mutation operation is designed to preserve the Gaussian nature of the noise
\[x^{\rm child}_T = \sqrt{1-\beta^2}x_{T}^{\rm parent} + \beta \epsilon_T, \quad \epsilon_T \sim \mathcal{N}(0,I),\]
where \(\beta\) is a hyperparameter that controls the strength of added stochasticity to the parents. The first term ensures that the mutated children preserve the high-reward region density, while the second term encourages exploration.
Intermediate denoising state mutation: To synthesize meaningful variations while preserving the intrinsic structure of the latent state \(x_t\), we propose an alternative mutation operator inspired by the reverse-time SDE:
\[ x_t^{\rm child}=x^{\rm parent}_t+\sigma_t \epsilon_t, \quad \epsilon_t \sim \mathcal{N}(0,I), \]
where \(\sigma_t\) is the diffusion coefficient defined in reverse-time SDE, controlling the level of injected stochasticity.
@misc{he2025scaling,
title={Scaling Image and Video Generation via Test-Time Evolutionary Search},
author={Haoran He and Jiajun Liang and Xintao Wang and Pengfei Wan and Di Zhang and Kun Gai and Ling Pan},
year={2025},
eprint={2505.17618},
archivePrefix={arXiv},
primaryClass={cs.CV}
}