  Diffusion models proved to be powerful models for generative speech
enhancement. In recent SGMSE+ approaches, training involves a stochastic
differential equation for the diffusion process, adding both Gaussian and
environmental noise to the clean speech signal gradually. The speech
enhancement performance varies depending on the choice of the stochastic
differential equation that controls the evolution of the mean and the variance
along the diffusion processes when adding environmental and Gaussian noise. In
this work, we highlight that the scale of the variance is a dominant parameter
for speech enhancement performance and show that it controls the tradeoff
between noise attenuation and speech distortions. More concretely, we show that
a larger variance increases the noise attenuation and allows for reducing the
computational footprint, as fewer function evaluations for generating the
estimate are required
