We construct a continuous superprocess X on M
(R d) which is the unique weak Feller extension of the
empirical process of consistent k-point motions generated by a family of
differential operators. The process X differs from known
Dawson–Watanabe type, Fleming–Viot type and
Ornstein–Uhlenbeck type superprocesses. This new type of superprocess
provides a connection between stochastic flows and measure-valued processes,
and determines a stochastic coalescence which is similar to those of
Smoluchowski. Moreover, the support of X describes how an initial
measure on R d is transported under the flow. As an
example, the process realizes a viewpoint of Darling about the isotropic
stochastic flows under certain conditions.