Adaptive Linear Path Model-Based Diffusion

TL;DR

The paper tackles the challenge of tuning diffusion-based planners for robotic control, where variance-preserving schedules introduce coupled hyperparameters that hinder easy adaptation. It proposes Linear Path Model-Based Diffusion (LP-MBD), a flow-matching–inspired linear probability path that decouples scheduling parameters, together with Adaptive LP-MBD (ALP-MBD) which uses PPO to adjust diffusion steps $T$ and noise cap $\sigma_{\max}$ conditioned on the environment. The key contributions are (1) a decoupled, geometrically grounded LP-MBD formulation, (2) an RL-based adaptive scheduler (ALP-MBD) that improves robustness and efficiency, and (3) extensive evaluation across numerical tasks, Brax benchmarks, and mobile-robot trajectory tracking showing improved sample efficiency, adaptability, and real-time performance. Together, these methods offer a simpler, interpretable, and scalable diffusion-driven framework for planning and control in challenging robotic environments.

Abstract

The interest in combining model-based control approaches with diffusion models has been growing. Although we have seen many impressive robotic control results in difficult tasks, the performance of diffusion models is highly sensitive to the choice of scheduling parameters, making parameter tuning one of the most critical challenges. We introduce Linear Path Model-Based Diffusion (LP-MBD), which replaces the variance-preserving schedule with a flow-matching-inspired linear probability path. This yields a geometrically interpretable and decoupled parameterization that reduces tuning complexity and provides a stable foundation for adaptation. Building on this, we propose Adaptive LP-MBD (ALP-MBD), which leverages reinforcement learning to adjust diffusion steps and noise levels according to task complexity and environmental conditions. Across numerical studies, Brax benchmarks, and mobile-robot trajectory tracking, LP-MBD simplifies scheduling while maintaining strong performance, and ALP-MBD further improves robustness, adaptability, and real-time efficiency.

Figures (6)

• Figure 1: The left figure illustrates a simple scenario in which the red ego vehicle drives in an obstacle-free environment. The right figure depicts a more complex case, where the red ego vehicle attempts to overtake a white vehicle while simultaneously avoiding an approaching car from behind. In the latter scenario, additional safety constraints are imposed, typically requiring more diffusion steps to obtain an optimal trajectory.
• Figure 2: Overview of ALP-MBD. The environment provides the current state $s_t$ and reward $r_t$ to the adaptive noise scheduler, which outputs the noise scheduling parameters $a_t = (T_t, \sigma_{\max,t})$. These parameters are fed into LP-MBD to generate the control input $u_t$, which is applied to the environment.
• Figure 3: 1D examples. (Top) The same example as in pan2024modelbased. (Middle) A simple Gaussian objective function. (Bottom) A Gaussian mixture objective with two modes.
• Figure 4: The comparison of AVP-MBD and ALP-MBD. The white line represents the constraint $3x_0 - x_1 \geq 2.0$. The top row shows the result of VP-MBD, and the bottom row shows the results of ALP-MBD with estimated parameters. After 30 training steps, we get $\beta_0=0.000028$, $\beta_1=0.361$, $T=3$ for AVP-MBD and $\sigma_{\max}=2.11$, $T=3$ for ALP-MBD.
• Figure 5: ALP-MBD in trajectory following tasks for a mobile robot. The red point describes the start point, and the green point indicates the goal point. The black line shows the reference trajectory, and the gray rectangle is the obstacle.