# SAD-Flower: Flow Matching for Safe, Admissible, and Dynamically Consistent Planning

arXiv: https://arxiv.org/abs/2511.05355 · HTML: https://mlsanity.com/paper/2511.05355/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 57 of its 79 references that are in the map.
- First posted on arXiv 7 Nov 2025.

## Builds on (most cited first, 30 of 57)

- [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)
- [Photorealistic Text-to-Image Diffusion Models with Deep Language Understanding](https://mlsanity.com/paper/2205.11487/) (2022)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor](https://mlsanity.com/paper/1801.01290/) (2018)
- [Diffusion Policy: Visuomotor Policy Learning via Action Diffusion](https://mlsanity.com/paper/2303.04137/) (2023)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [OpenAI Gym](https://mlsanity.com/paper/1606.01540/) (2016)
- [D4RL: Datasets for Deep Data-Driven Reinforcement Learning](https://mlsanity.com/paper/2004.07219/) (2020)
- [Planning with Diffusion for Flexible Behavior Synthesis](https://mlsanity.com/paper/2205.09991/) (2022)
- [Building Normalizing Flows with Stochastic Interpolants](https://mlsanity.com/paper/2209.15571/) (2022)
- [AudioLDM: Text-to-Audio Generation with Latent Diffusion Models](https://mlsanity.com/paper/2301.12503/) (2023)
- [Is Conditional Generative Modeling all you need for Decision-Making?](https://mlsanity.com/paper/2211.15657/) (2022)
- [Lipschitz regularity of deep neural networks: analysis and efficient estimation](https://mlsanity.com/paper/1805.10965/) (2018)
- [PhysDiff: Physics-Guided Human Motion Diffusion Model](https://mlsanity.com/paper/2212.02500/) (2022)
- [Efficient and Accurate Estimation of Lipschitz Constants for Deep Neural Networks](https://mlsanity.com/paper/1906.04893/) (2019)
- [Control Barrier Function Based Quadratic Programs for Safety Critical Systems](https://mlsanity.com/paper/1609.06408/) (2016)
- [Learning to Act from Actionless Videos through Dense Correspondences](https://mlsanity.com/paper/2310.08576/) (2023)
- [Motion Planning Diffusion: Learning and Planning of Robot Motions with Diffusion Models](https://mlsanity.com/paper/2308.01557/) (2023)
- [PDDLStream: Integrating Symbolic Planners and Blackbox Samplers via Optimistic Adaptive Planning](https://mlsanity.com/paper/1802.08705/) (2018)
- [Guided Flows for Generative Modeling and Decision Making](https://mlsanity.com/paper/2311.13443/) (2023)
- [Efficient Model-Based Reinforcement Learning through Optimistic Policy Search and Planning](https://mlsanity.com/paper/2006.08684/) (2020)
- [Diffusion Models Beat GANs on Topology Optimization](https://mlsanity.com/paper/2208.09591/) (2022)
- [SafeDiffuser: Safe Planning with Diffusion Probabilistic Models](https://mlsanity.com/paper/2306.00148/) (2023)
- [Uniform Error Bounds for Gaussian Process Regression with Application to Safe Control](https://mlsanity.com/paper/1906.01376/) (2019)
- [Aligning Optimization Trajectories with Diffusion Models for Constrained Design Generation](https://mlsanity.com/paper/2305.18470/) (2023)

## Built on by (most cited first, 3 of 3)

- [From Demonstrations to Safe Deployment: Path-Consistent Safety Filtering for Diffusion Policies](https://mlsanity.com/paper/2511.06385/) (2025)
- [PC-Diffuser: Path-Consistent Capsule CBF Safety Filtering for Diffusion-Based Trajectory Planner](https://mlsanity.com/paper/2603.10330/) (2026)
- [LyapuFlow: Controlling Generative Flows with Lyapunov Feedback for Inverse Problems](https://mlsanity.com/paper/2610.04326/) (2026)

## Abstract (arXiv)

Flow matching (FM) has shown promising results in data-driven planning. However, it inherently lacks formal guarantees for ensuring state and action constraints, whose satisfaction is a fundamental and crucial requirement for the safety and admissibility of planned trajectories on various systems. Moreover, existing FM planners do not ensure the dynamical consistency, which potentially renders trajectories inexecutable. We address these shortcomings by proposing SAD-Flower, a novel framework for generating Safe, Admissible, and Dynamically consistent trajectories. Our approach relies on an augmentation of the flow with a virtual control input. Thereby, principled guidance can be derived using techniques from nonlinear control theory, providing formal guarantees for state constraints, action constraints, and dynamic consistency. Crucially, SAD-Flower operates without retraining, enabling test-time satisfaction of unseen constraints. Through extensive experiments across several tasks, we demonstrate that SAD-Flower outperforms various generative-model-based baselines in ensuring constraint satisfaction.