ICML 2025

Local Manifold Approximation and Projection
for Manifold-Aware Diffusion Planning
Kyowoon Lee 1 Jaesik Choi 1 2
Abstract
Recent advances in diffusion-based generative
modeling have demonstrated significant promise
in tackling long-horizon, sparse-reward tasks
by leveraging offline datasets. While these ap-
proaches have achieved promising results, their
reliability remains inconsistent due to the inherent
stochastic risk of producing infeasible trajectories,
limiting their applicability in safety-critical appli-
cations. We identify that the primary cause of
these failures is inaccurate guidance during the
sampling procedure, and demonstrate the exis-
tence of manifold deviation by deriving a lower
bound on the guidance gap. To address this chal-
lenge, we propose Local Manifold Approximation
and Projection (LoMAP), a training-free method
that projects the guided sample onto a low-rank
subspace approximated from offline datasets, pre-
venting infeasible trajectory generation. We val-
idate our approach on standard offline reinforce-
ment learning benchmarks that involve challeng-
ing long-horizon planning. Furthermore, we show
that, as a standalone module, LoMAP can be in-
corporated into the hierarchical diffusion planner,
providing further performance enhancements.
1. Introduction
Planning over long horizons is crucial for autonomous sys-
tems operating in real-world settings, where rewards are
sparse and actions often entail delayed consequences (Lee
et al., 2023a). When environment dynamics are fully known,
methods such as Model Predictive Control (Tassa et al.,
2012) and Monte Carlo Tree Search (Silver et al., 2016;
2017; Lee et al., 2018) have achieved remarkable success.
In most practical applications, however, the dynamics are
1Korea Advanced Institute of Science and Technology
(KAIST)
2INEEJI. Correspondence to:
Jaesik Choi <jae-
sik.choi@kaist.ac.kr>.
Proceedings of the 42 nd International Conference on Machine
Learning, Vancouver, Canada. PMLR 267, 2025. ...