  In this note, we prove a uniform distance distortion estimate for Ricci flows
with uniformly bounded scalar curvature, independent of the lower bound of the
initial $\mu$-entropy. Our basic principle tells that once correctly
renormalized, the metric-measure quantities obey similar estimates as in the
non-collapsing case; espeically, the lower bounds of the renormalized heat
kernel, observed on a scale comparable to the initial diameter, matches with
the lower bound of the renormalized volume ratio, giving the desired distance
distortion estimate.
