We introduce FLOWER, a novel conditioning method designed for speech restoration that integrates Gaussian guidance into generative frameworks. By transforming clean speech into a predefined prior distribution (e.g., Gaussian distribution) using a normalizing flow network, FLOWER extracts critical information to guide generative models. This guidance is incorporated into each block of the generative network, enabling precise restoration control. Experimental results demonstrate the effectiveness of FLOWER in improving performance across various general speech restoration tasks.