Generative AI using diffusion models has proved to be very effective in creating synthetic images, videos, text, speech and other data. Its impact on recent AI algorithms has been revolutionary. Impressive algorithms have emerged on the Generative AI landscape over the last decade. In these models, synthetic data are progressively refined by the time reversal of certain forward diffusion processes. A key bottleneck in this technology is the lack of a theory for directly reversing these diffusion processes and current implementation deploys indirect approaches. These indirect time reversals are inaccurate, inefficient, slow and computationally onerous. A theory for direct reversal of these diffusion processes is sorely needed and will not only significantly improve Generative AI algorithms but will also constitute a foundational advance to the theory of diffusions. The diffusion models to be time reversed in Generative AI are stochastic difference equations. While the theory of reversing a stochastic differential equation (SDE) was formulated by Anderson in 1982, no comparable theory exists for difference equations. Instead, an indirect approach comprising three steps is employed. A stochastic difference equation is first approximated by a differential equation. It is then reversed using Anderson’s theory. The final step discretizes this reverse differential equation. This use of an approximation of another approximation has many issues. Approximations always induce errors.