The asymmetry of gravity and its relationship to the arrow of time is a fundamental question in physics. This paper explores this connection from the perspective of spacetime energy diffusion, proposing a mechanism by which the asymmetry of the gravitational field induces energy diffusion, leading to the emergence of irreversibility of time on macroscopic scales. The theory is developed through a detailed derivation of the energy diffusion equation, incorporating the effects of spacetime curvature via the connection coefficients. A curvature-dependent diffusion coefficient is introduced to quantify the effect of curvature on energy diffusion rates. The entropy production rate is separated into thermal and gravitational contributions, providing a new perspective on the thermodynamic arrow of time. The potential impact of quantum gravity effects in regions of extreme spacetime curvature is also considered, suggesting possible modifications to the classical energy diffusion equation. The theory is consistent with the thermodynamic arrow of time and opens up new avenues for exploring the deep connections between gravity, quantum mechanics, and the nature of time. Future research directions include connecting this theory to fundamental physics, exploring applications to the early universe, and pursuing experimental and observational verification.