Analytic Bridge Diffusions for Controlled Path Generation
The LQ-GM-PID method is an innovative approach in bridge-diffusion techniques that enables finite-time transport with clear solutions for scores, intermediate marginals, and protocol gradients, eliminating the need for neural networks or internal stochastic simulations. It transforms the classic linear-quadratic-Gaussian (LQG) stochastic-control model into a Path Integral Diffusion (PID) transport problem. In this framework, linear dynamics combined with Gaussian noise and quadratic costs lead to Riccati equations, allowing for optimal feedback in a closed form, where the focus shifts from regulating terminal states to achieving a specified terminal distribution. While it does have some limitations, it offers enough versatility for producing controlled paths.
Key facts
- Method is called LQ-GM-PID.
- It is a bridge-diffusion method for finite-time transport.
- Scores, intermediate marginals, and protocol gradients are available in closed form.
- No neural networks are needed in the optimization loop.
- No inner stochastic simulation loops are required.
- It recasts LQG stochastic control as a PID transport problem.
- Linear dynamics, Gaussian noise, and quadratic costs are assumed.
- Terminal state regulation is replaced by a prescribed terminal distribution.
Entities
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