Resolving the $H_0$ tension with diffusion

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.