  The paper is an attempt to relate two vast areas of the applicability of the
renormalization group (RG): field theoretic models and partial differential
equations. It is shown that the Green function of a nonlinear diffusion
equation can be viewed as a correlation function in a field-theoretic model
with an ultralocal term, concentrated at a spacetime point. This field theory
is shown to be multiplicatively renormalizable, so that the RG equations can be
derived in a standard fashion, and the RG functions (the $\beta$ function and
anomalous dimensions) can be calculated within a controlled approximation. A
direct calculation carried out in the two-loop approximation for the
nonlinearity of the form $\phi^{\alpha}$, where $\alpha>1$ is not necessarily
integer, confirms the validity and self-consistency of the approach. The
explicit self-similar solution is obtained for the infrared asymptotic region,
with exactly known exponents; its range of validity and relationship to
previous treatments are briefly discussed.
