The traditional method of performing renormalization group (RG) transformations for spin systems is by spin-blocking, where the block spins are local averages of the original spins, and they live on a lattice with fewer sites than the original lattice. As such, this transformation is inherently discrete. By contrast, over the last decade a new technique known as “gradient flow” has been introduced in lattice theory that has enjoyed several applications, and which consists of diffusing the lattice field by a heat-like equation. By suitably interpreting this gradient flow, one can define a “continuous blocking” of the lattice field which suggests new methods for obtaining critical exponents of lattice systems near criticality. In this talk, I will discuss this new approach to RG on the lattice, and its connection to the program of functional RG.