  The tension between the value of the Hubble constant $H_0$ determined from
local supernovae data and the one inferred from the cosmic microwave background
based on the $\Lambda$CDM cosmological model may indicate the need for new
physics. Here, we show that this `Hubble tension' can be resolved in models
involving an effective energy flux from the matter sector into dark energy
resulting naturally from a combination of unimodular gravity and an energy
diffusion process. The scheme is one where dark energy has the standard
equation of state $w=-1$. This proposal provides an alternative
phenomenological paradigm accounting for the observations, while offering a
general framework to study diffusion effects coming from novel fundamental
physical processes.
