# LTLDoG: Satisfying Temporally-Extended Symbolic Constraints for Safe Diffusion-based Planning

arXiv: https://arxiv.org/abs/2405.04235 · HTML: https://mlsanity.com/paper/2405.04235/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 42 references that are in the map.
- First posted on arXiv 7 May 2024.

## Builds on (most cited first, 25 of 25)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Diffusion Policy: Visuomotor Policy Learning via Action Diffusion](https://mlsanity.com/paper/2303.04137/) (2023)
- [Modeling Relational Data with Graph Convolutional Networks](https://mlsanity.com/paper/1703.06103/) (2017)
- [D4RL: Datasets for Deep Data-Driven Reinforcement Learning](https://mlsanity.com/paper/2004.07219/) (2020)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [Planning with Diffusion for Flexible Behavior Synthesis](https://mlsanity.com/paper/2205.09991/) (2022)
- [Is Conditional Generative Modeling all you need for Decision-Making?](https://mlsanity.com/paper/2211.15657/) (2022)
- [Improving Diffusion Models for Inverse Problems using Manifold Constraints](https://mlsanity.com/paper/2206.00941/) (2022)
- [Score-based diffusion models for accelerated MRI](https://mlsanity.com/paper/2110.05243/) (2021)
- [Come-Closer-Diffuse-Faster: Accelerating Conditional Diffusion Models for Inverse Problems through Stochastic Contraction](https://mlsanity.com/paper/2112.05146/) (2021)
- [Robust Compressed Sensing MRI with Deep Generative Priors](https://mlsanity.com/paper/2108.01368/) (2021)
- [SafeDiffuser: Safe Planning with Diffusion Probabilistic Models](https://mlsanity.com/paper/2306.00148/) (2023)
- [LTL2Action: Generalizing LTL Instructions for Multi-Task RL](https://mlsanity.com/paper/2102.06858/) (2021)
- [Backpropagation through Signal Temporal Logic Specifications: Infusing Logical Structure into Gradient-Based Methods](https://mlsanity.com/paper/2008.00097/) (2020)
- [Symbolic LTLf Synthesis](https://mlsanity.com/paper/1705.08426/) (2017)
- [Don't Start from Scratch: Behavioral Refinement via Interpolant-based Policy Diffusion](https://mlsanity.com/paper/2402.16075/) (2024)
- [Policy Optimization with Linear Temporal Logic Constraints](https://mlsanity.com/paper/2206.09546/) (2022)
- [On the (In)Tractability of Reinforcement Learning for LTL Objectives](https://mlsanity.com/paper/2111.12679/) (2021)
- [Trajectory Generation, Control, and Safety with Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2306.15512/) (2023)
- [Embedding Symbolic Temporal Knowledge into Deep Sequential Models](https://mlsanity.com/paper/2101.11981/) (2021)
- [Temporal Logic Motion Planning with Convex Optimization via Graphs of Convex Sets](https://mlsanity.com/paper/2301.07773/) (2023)

## Built on by (most cited first, 16 of 16)

- [Diffusion Model for Planning: A Systematic Literature Review](https://mlsanity.com/paper/2408.10266/) (2024)
- [TeLoGraF: Temporal Logic Planning via Graph-encoded Flow Matching](https://mlsanity.com/paper/2505.00562/) (2025)
- [Diffusion Meets Options: Hierarchical Generative Skill Composition for Temporally-Extended Tasks](https://mlsanity.com/paper/2410.02389/) (2024)
- [Projected Coupled Diffusion for Test-Time Constrained Joint Generation](https://mlsanity.com/paper/2508.10531/) (2025)
- [Zero-Shot Trajectory Planning for Signal Temporal Logic Tasks](https://mlsanity.com/paper/2501.13457/) (2025)
- [DDPS: Discrete Diffusion Posterior Sampling for Paths in Layered Graphs](https://mlsanity.com/paper/2504.20754/) (2025)
- [Compositional Visual Planning via Inference-Time Diffusion Scaling](https://mlsanity.com/paper/2603.02646/) (2026)
- [Inference-Time Attribute Distribution Alignment for Unconditional Diffusion](https://mlsanity.com/paper/2605.07456/) (2026)
- [DiRecT: Safe Diffusion-Based Planning via Receding-Horizon Denoising](https://mlsanity.com/paper/2606.15359/) (2026)
- [Robust Planning for Autonomous Driving via Mixed Adversarial Diffusion Predictions](https://mlsanity.com/paper/2505.12327/) (2025)
- [Multi-Robot Motion Planning from Vision and Language using Heat-Inspired Diffusion](https://mlsanity.com/paper/2512.13090/) (2025)
- [Guided Streaming Stochastic Interpolant Policy](https://mlsanity.com/paper/2605.10051/) (2026)
- [Generalizable Multi-Agent Planning from Signal Temporal Logic Specifications via Diffusion](https://mlsanity.com/paper/2608.29490/) (2026)
- [LTLDiff: Finite Linear Temporal Logic-Guided Data Generation and Diffusion Policies for Multi-agent Robotic Manipulation](https://mlsanity.com/paper/2609.11043/) (2026)
- [Jaxolotl: A Unified High-Performance Benchmark Suite for LTL-Based Multi-Task RL](https://mlsanity.com/paper/2609.38065/) (2026)
- [Learning Task and Motion Plans from Real Demonstrations with Hybrid Flow Matching](https://mlsanity.com/paper/2610.04771/) (2026)

## Abstract (arXiv)

Operating effectively in complex environments while complying with specified constraints is crucial for the safe and successful deployment of robots that interact with and operate around people. In this work, we focus on generating long-horizon trajectories that adhere to novel static and temporally-extended constraints/instructions at test time. We propose a data-driven diffusion-based framework, LTLDoG, that modifies the inference steps of the reverse process given an instruction specified using finite linear temporal logic (LTLf). LTLDoG leverages a satisfaction value function on LTLf and guides the sampling steps using its gradient field. This value function can also be trained to generalize to new instructions not observed during training, enabling flexible test-time adaptability. Experiments in robot navigation and manipulation illustrate that the method is able to generate trajectories that satisfy formulae that specify obstacle avoidance and visitation sequences. Code and supplementary material are available online at https://github.com/clear-nus/ltldog.