Tabula Rasa: Monte Carlo estimation of unit-variance noise with controlled spatio-temporal correlation

2026-10-08

AI Summary

This study addresses the critical need in downstream tasks for time-varying Gaussian noise with controlled variance and temporal correlation, a requirement that existing generation methods struggle to satisfy due to high computational complexity and inadequate temporal consistency. To overcome these limitations, this work introduces database sketching theory to unify pixel reconstruction and variance estimation into a joint Monte Carlo estimation problem, thereby enabling efficient modeling and generation of Gaussian noise. The proposed framework substantially simplifies implementation logic and significantly improves execution efficiency. Compared to existing baselines, our approach achieves superior noise control through a more concise implementation, effectively enhancing both temporal consistency and controllability for downstream applications.

Abstract

We suggest a method to generate time-varying Gaussian noise with controlled variance and controlled temporal correlation. This noise is used in several downstream tasks for temporal control and temporal coherence. The core technical idea is to phrase this problem as joint Monte-Carlo estimation of both a classic pixel reconstruction and estimation of variance using the concept of "sketching" from the database literature. We demonstrate that our method allows temporal control for downstream tasks with simpler and faster code than previous methods.

Problem

• Gaussian noise
• temporal correlation
• variance control
• temporal coherence
• Monte Carlo estimation

Innovation

• Monte Carlo estimation
• Gaussian noise
• spatio-temporal correlation
• sketching
• variance estimation