GuideFlow: Constraint-Guided Flow Matching for Planning in End-to-End Autonomous Driving¶

Conference: CVPR 2026
Paper: CVF Open Access
Code: https://github.com/adept-thu/GuideFlow (Coming Soon)
Area: End-to-End Autonomous Driving / Trajectory Planning
Keywords: End-to-end driving planning, Flow matching, Constrained generation, Energy-based models, Mode collapse

TL;DR¶

GuideFlow employs "Flow Matching + Energy-Based Models" for end-to-end driving planning, directly embedding safety and physical hard constraints into the generation process via three mechanisms: Constrained Velocity Field (CVF), Constrained Flow states (CF), and Refining the Flow by EBM (RFE). This approach mitigates multi-modal mode collapse in imitation learning and eliminates the need for post-optimization in generative methods, achieving a SOTA 43.0 EPDMS on NavSim Navhard.

Background & Motivation¶

Background: End-to-end autonomous driving (E2E-AD) integrates perception, prediction, and planning into a jointly trained differentiable system, where the planning module predicts feasible trajectories. To reflect the multi-intent uncertainty of real-world driving, planning has shifted from single-modal to multi-modal trajectory generation, primarily divided into imitative and generative approaches.

Limitations of Prior Work: Both paradigms have critical drawbacks. Imitative planners (e.g., UniAD, VAD, SparseDrive) use L2/Huber losses to regress expert trajectories, but since each scene has only one Ground Truth (GT) for supervision, the nominal multi-modal outputs often collapse toward a single dominant mode—known as mode collapse. Generative planners (e.g., DiffusionDrive, DiffusionPlanner) sample from learned distributions to express multi-modality, but the randomness and high variance of the sampling process cannot guarantee that generated trajectories satisfy hard constraints such as collisions, lane boundaries, or kinematics, often requiring an unreliable post-optimization stage.

Key Challenge: There is a tension between "diversity" in generative methods and "constraint satisfaction"—implicitly encoding constraints into a latent space is neither interpretable nor easily enforced during sampling, while explicitly forcing trajectory points (per-step projection) severely disrupts the probabilistic path of sampling.

Goal: To achieve (1) multi-modal diversity, (2) explicit hard constraint satisfaction, and (3) controllable driving styles within a single generative framework without independent post-optimization.

Key Insight: The authors select Rectified Flow as the generative backbone, which learns a near-linear transport path between prior and target distributions for fast and stable sampling. They observe that each trajectory update $x^{(k+1)}$ depends on the velocity field $v_\theta$, the previous flow state $x^{(k)}$, and an energy term $E_\theta$ in the refinement stage. Thus, constraints can be injected at these three intervention points.

Core Idea: Instead of letting the model learn constraints implicitly, this work explicitly carves constraints into the flow matching generation process by correcting the velocity field direction, replacing flow states with constrained anchors mid-sampling, and utilizing energy models to define "violation = high energy," ensuring samples naturally land in the feasible region.

Method¶

Overall Architecture¶

GuideFlow is a flow-matching-based trajectory generator. Multi-view images are processed by a perception module to obtain BEV representations, which are parsed into Agent tokens (dynamic interactions) and Map tokens (road/lane topology). A trajectory is represented as a flow state $x_t \in \mathbb{R}^{T \times 2}$ (where $T$ is the prediction horizon), fused with scene tokens via cross-attention, and integrated with classifier-free intent/reward conditions to decode the velocity field $v_\theta(x_t, t)$. Finally, during sampling, three constraint strategies (CVF, CF, RFE) correct the velocity field and flow path to integrate the final trajectory.

%%{init: {'flowchart': {'rankSpacing': 24, 'nodeSpacing': 28, 'padding': 6, 'wrappingWidth': 400, 'subGraphTitleMargin': {'top': 8, 'bottom': 16}}}}%%
flowchart TD
    A["Multi-view Images"] --> B["Perception Encoding<br/>BEV → Agent/Map tokens"]
    B --> C["Perception-Conditioned Flow Matching Generator<br/>Cross-attention Fusion → Velocity Field vt"]
    C --> D["Classifier-free Intent & Reward Guidance<br/>plan anchor / goal / command / reward"]
    D --> E
    subgraph E["Three Strategies for Constrained Generation"]
        direction TB
        E1["CVF Constrained Velocity Field"] --> E2["CF Constrained Flow States"] --> E3["RFE Energy Model Refinement"]
    end
    E --> F["Reward as Style<br/>Aggressiveness EP Adjustment"]
    F --> G["Feasible + Safe Trajectory τ"]

Key Designs¶

1. Perception-Conditioned Flow Matching Generator: Mitigating mode collapse from the source

Imitative planners suffer from mode collapse due to L2 supervision on a single GT per scene. GuideFlow adopts Rectified Flow, constructing a linear probability path $x_t = (1-t)x_0 + tx_1$ between a Gaussian prior $\pi_0$ and the target distribution $\pi_1$. The training objective is $L_{RF} = \mathbb{E}_{t,x_0,x_1} \lVert v_\theta(x_t, t) - (x_1 - x_0) \rVert^2$, and inference uses numerical integration $x^{(k+1)} = x^{(k)} + v_\theta(x^{(k)}, t_k) \Delta t$. Starting from random noise and guided by diverse conditions, it naturally generates multi-modal hypotheses.

To prevent it from favoring only dominant modes, the authors utilize Energy Matching, treating the flow model as an energy-based model (EBM) at $t > 1$ with an energy weight $\varepsilon(t)$. This shapes the manifold into multiple low-energy basins (e.g., yielding vs. merging), with updates becoming $x^{(k+1)} = x^{(k)} + v_\theta \Delta t - \eta(t_k) \nabla_x E_\theta(x^{(k)})$.

2. Classifier-free Intent and Reward Guidance: High-quality starting points for constraints

GuideFlow uses four types of dynamic signals: plan anchor $C_p$, goal point $C_g$, driving command $C_d$, and reward $C_r$ (style). Plan anchors are curated from an $N=256$ trajectory vocabulary $V_a$. During sampling, $N$ diverse candidates are generated based on these anchors. Guidance uses the classifier-free approach: $v_\theta^{guide} = (1-\gamma)v_\theta(x_t, t) + \gamma v_\theta(x_t, t, c)$, where $\gamma$ scales the condition strength.

3. Three Strategies for Constrained Generation (CVF/CF/RFE): Embedding hard constraints into generation

CVF (Constraining the Velocity Field): Selects a feasible trajectory $x_1^c$ from anchors and calculates the ideal field $v_t^c = \frac{x_1^c - x_0}{1 - 0}$. The predicted field is corrected toward it: $$v_t^* = v_t - 2\lambda \frac{v_t \cdot v_t^c}{\lVert v_t^c \rVert^2} v_t^c, \qquad \lambda=0.1$$
CF (Constraining the Flow States): Instead of step-wise correction, it performs a single intervention at step $k_c$ by replacing $x^{(k_c)}$ with the constrained anchor $x_1^c$, then resuming sampling. This late-stage correction ensures feasibility without disrupting the learned transport dynamics.
RFE (Refining the Flow by EBM): Defines energy as $E_\theta(x_t) = \lVert \jmath(f_{t>1}(x_t)) - \jmath(x_t) \rVert^2$, where $\jmath(\cdot)$ evaluates constraint satisfaction. The objective $L_{RFE} = E_\theta(x^{(1)}) - E_\theta(x_1)$ penalizes violations, allowing the model to implicitly learn constraint awareness.

4. Reward as Style: Driving style as a controllable knob

An Aggressiveness Score (EP) is defined based on the distance traveled along the lane centerline. Tuning EP toward 1 generates more aggressive behavior, turning "style" into an explicit, controllable signal.

Loss & Training¶

The total loss consists of the flow matching term $L_{RF}$ and the energy refinement term $L_{RFE}$. Training spans 100 epochs for NavSim (ResNet34 backbone), 8 epochs for NuScenes (SparseDrive-based), and 20 epochs for Bench2Drive.

Key Experimental Results¶

Main Results¶

NavSim Navhard (Closed-loop, higher EPDMS is better):

Config	Backbone	Scorer	EPDMS	Notes
LTF	ResNet34	None	23.1	Imitation baseline
DiffusionDrive	ResNet34	None	24.2	Diffusion-based
GuideFlow	ResNet34	None	27.1	Outperforms without scorer
DriveSuprim	V2-99	Yes	42.1	Previous SOTA
GuideFlow + Scorer	ResNet34	Yes	43.0	SOTA, +1.3

Bench2Drive & NuScenes:

Dataset	Metric	Ours	Prev. SOTA	Gain
Bench2Drive	Driving Score ↑	75.21	73.86	+1.35
NuScenes	Avg. Collision ↓	0.07%	0.08%	-0.01%

Ablation Study¶

Constraint Modules (NavSim Navhard, EPDMS): | Config | EPDMS | Note | |------|-------|------| | Baseline | 23.1 | No constraints | | + CVF | 24.5 | Step-wise correction | | + CF | 25.1 | Single truncation (Better than CVF) | | + RFE | 25.5 | Energy refinement (max OOD gain) | | + CF + RFE | 27.1 | Best combination |

Key Findings¶

CF > CVF: Step-wise correction (CVF) disrupts the probability path; single intervention (CF) at step $k_c=50$ provides better generation quality and adaptation.
RFE for OOD: Energy matching scales well to out-of-distribution (OOD) scenarios by defining generalizable constraint rules.
Style vs. Safety: Increasing aggressiveness (EP) improves speed but slightly reduces EPDMS, indicating a trade-off.

Highlights & Insights¶

Mechanism Decomposition: By identifying the components of the update equation (field, state, energy), the work provides a clean paradigm for where to inject constraints.
One-time Correction (CF): The idea of a single truncation mid-sampling is a clever solution to balancing hard constraints with probabilistic path smoothness.
EBM Integration: Unifying flow matching with energy landscapes turns "violation" into a trainable signal rather than just an inference-time heuristic.

Limitations & Future Work¶

The trade-off between style and safety remains an open challenge.
Reliance on anchor quality: CVF/CF depends on the reference anchor $x_1^c$; if the reference is suboptimal, the correction is also capped.
Inference speed: At 3.6 FPS (RTX 4090), it is slower than imitative models like SparseDrive (9.0 FPS).
Expanding energy proxies to incorporate complex social and traffic laws.

vs. Imitative Planners: GuideFlow avoids mode collapse by design using conditional flow matching rather than deterministic regression.
vs. DiffusionDrive/Planner: Unlike methods that only refine at the end or add energy bias during inference, GuideFlow explicitly supervises the generation process and integrates energy gradients directly into the flow dynamics.

Rating¶

Novelty: ⭐⭐⭐⭐⭐
Experimental Thoroughness: ⭐⭐⭐⭐⭐
Writing Quality: ⭐⭐⭐⭐
Value: ⭐⭐⭐⭐⭐