  We generalize the quantum Fisher information flow proposed by Lu \textit{et
al}. [Phys. Rev. A \textbf{82}, 042103 (2010)] to the multi-parameter scenario
from the information geometry perspective. A measure named the
\textit{intrinsic density flow} (IDF) is defined with the time-variation of the
intrinsic density of quantum states (IDQS). IDQS measures the local
distinguishability of quantum states in state manifolds. The validity of IDF is
clarified with its vanishing under the parameter-independent unitary evolution
and outward-flow (negativity) under the completely positive-divisible map. The
temporary backflow (positivity) of IDF is thus an essential signature of the
non-Markovian dynamics. Specific for the time-local master equation, the IDF
decomposes according to the channels, and the positive decay rate indicates the
inwards flow of the sub-IDF. As time-dependent scalar fields equipped on the
state space, the distribution of IDQS and IDF comprehensively illustrates the
distortion of state space induced by its environment. As example, a typical
qubit model is given.
