CCS: Controllable and Constrained Sampling with Diffusion Models via Initial Noise Perturbation
This work addresses the controllability of diffusion models for generative tasks, which is an incremental improvement for researchers and practitioners in machine learning.
The authors tackled the problem of controlling the sampling process in diffusion models by investigating the linear relationship between initial noise perturbation and generated outputs, proposing a Controllable and Constrained Sampling (CCS) method that achieves more precise control while maintaining superior sample quality and diversity.
Diffusion models have emerged as powerful tools for generative tasks, producing high-quality outputs across diverse domains. However, how the generated data responds to the initial noise perturbation in diffusion models remains under-explored, which hinders understanding the controllability of the sampling process. In this work, we first observe an interesting phenomenon: the relationship between the change of generation outputs and the scale of initial noise perturbation is highly linear through the diffusion ODE sampling. Then we provide both theoretical and empirical study to justify this linearity property of this input-output (noise-generation data) relationship. Inspired by these new insights, we propose a novel Controllable and Constrained Sampling method (CCS) together with a new controller algorithm for diffusion models to sample with desired statistical properties while preserving good sample quality. We perform extensive experiments to compare our proposed sampling approach with other methods on both sampling controllability and sampled data quality. Results show that our CCS method achieves more precisely controlled sampling while maintaining superior sample quality and diversity.