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By [[Fokker–Planck equation|Fokker-Planck equation]], the density of the cloud evolves according to<math display="block">\partial_t \ln \rho_t = \frac 12 \beta(t) \left(
n + (x+ \nabla\ln\rho_t) \cdot \nabla \ln\rho_t + \Delta\ln\rho_t
\right)</math>where <math>n</math> is the dimension of space, and <math>\Delta</math> is the [[Laplace operator]]. Equivalently,<math display="block">\partial_t \rho_t = \frac 12 \beta(t) ( \nabla\cdot(x\rho_t) + \Delta \rho_t)</math>
==== Backward diffusion process ====
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