Cross-Scenario Controller Parameter Transformation from Real-World Driving Data through Flow Matching

Christian Zink; Maik Pfefferkorn; Eric Lenz; Felix Kallmeyer; Rolf Findeisen

eess.SYOct 23, 2026

Cross-Scenario Controller Parameter Transformation from Real-World Driving Data through Flow Matching

Authors: Christian Zink, Maik Pfefferkorn, Eric Lenz, Felix Kallmeyer, Rolf Findeisen

Organizations: Control and Cyber-Physical Systems Laboratory, Technical University of Darmstadt, Darmstadt, Germany · Driver Assistance Systems Predevelopment, Volkswagen AG, Wolfsburg, Germany

Abstract

Advanced Driver Assistance Systems have become increasingly widespread, aiming to support drivers, reduce workload, and improve traffic safety. However, many systems are rarely used because their behavior feels unnatural and does not match individual driving behavior. The growing availability of large-scale, real-world human driving data enables more human-like and driver-individual assistance functions. This paper formulates the adaptation of Adaptive Cruise Control parameters as a driver-individual scenario-to-scenario transport problem, transforming controller parameters from one driving context to another. Using flow matching, we train a generative model to predict the target-scenario behavior of previously unseen drivers from only a few demonstrations in a source scenario. We compare the approach with a linear parameter-shift baseline and evaluate flow-matching variants incorporating driver-consistent coupling, driver embeddings, and classifier-free guidance based on driving profiles extracted from trajectory data using a variational autoencoder.

Figures & tables

Fig. 1: The ego vehicle (red) is either approaching (decreasing distance) or following (maintaining a nearly constant distance) the preceding vehicle (blue).

D

denotes the inter-vehicle distance, while

v_{-1}

and

v

represent the velocities of the preceding and ego vehicle, respectively.

Panel of Figure 2 — Fig. 2: Transformer-based $\beta$ -VAE with Set-Aggregator

Fig. 3: UMAP projection of the latent space reparameterization from the per-trajectory profiles.

Fig. 4: Parameter distributions (

K_{\mathrm{P}},K_{\mathrm{D}}

) for

\mathcal{D}_{\mathrm{slow}}

and

\mathcal{D}_{\mathrm{fast}}

approach maneuvers and the generated parameter distributions

\mathcal{D}_{\mathrm{\Delta}}

and

\mathcal{D}_{\mathrm{FM}}

\mathcal{D}_{\mathrm{\Delta}}^{(m=0)}

and

\mathcal{D}_{\mathrm{FM}}^{(m=0)}

are the analyzed parameter points.

Fig. 5: Transformation from

\mathcal{D}_{\mathrm{slow}}^{\mathrm{mdl}}

\mathcal{D}_{\Delta}

and

\mathcal{D}_{\mathrm{FM}}

compared to a real-world fast approach scenario

\mathcal{D}_{\mathrm{fast}}^{\mathrm{meas}}

Model	$W_{2}^{\mathrm{norm}}$	$\Delta\mu^{\mathrm{norm}}$	$\\|\Delta\Sigma\\|_{F}^{\mathrm{norm}}$
Linear	$1.00\pm 0.00$	$1.00\pm 0.00$	$1.00\pm 0.00$
FM	$0.18\pm 0.02$	$\hbox to21.78pt{\vbox to10.44pt{\pgfpicture\makeatletter\hbox{\hskip 10.88892pt\lower-5.22221pt\hbox to0.0pt{\lxSVG@begingroup@{_scopebegin=1} \lxSVG@begingroup@{stroke=#000000} \lxSVG@begingroup@{fill=#000000} \lxSVG@setlinewidth{\the\pgflinewidth}\lxSVG@begingroup@{stroke-width=0.4pt} \lx@inpgf@ignorespaces\nullfont\lxSVG@begingroup@{_scopebegin=1} \lxSVG@closescope \hbox to0.0pt{\lxSVG@begingroup@{_scopebegin=1} { {{}}\lx@inpgf@ignorespaces\hbox{\hbox{{\lxSVG@begingroup@{_scopebegin=1} \lxSVG@setlinewidth{\the\pgflinewidth}\lxSVG@begingroup@{stroke-width=0.4pt} \lx@inpgf@ignorespaces{{}{}{{ {}{}}}{ {}{}} {{}{{\lx@inpgf@ignorespaces}}}{{}{\lx@inpgf@ignorespaces}}{}{{}{\lx@inpgf@ignorespaces}} {\lxSVG@begingroup@{_scopebegin=1} \lxSVG@setlinewidth{\the\pgflinewidth}\lxSVG@begingroup@{stroke-width=0.4pt} \lx@inpgf@ignorespaces{}\lxSVG@stroke\lxSVG@drawpath@unclipped{M -14.79 -6.95 h 29.58 v 13.9 h -29.58 Z}{fill:none} \lx@inpgf@ignorespaces \lxSVG@closescope }{{{{\lx@inpgf@ignorespaces}}\lxSVG@begingroup@{_scopebegin=1} \lxSVG@transformcm{1.0}{0.0}{0.0}{1.0}{-8.88892pt}{-3.22221pt}\lxSVG@begingroup@{transform=matrix(1.0 0.0 0.0 1.0 -12.3 -4.46)} \pgfsys@hbox{58}\lxSVG@closescope }}} \lxSVG@closescope }}} } \lxSVG@closescope {{ {}{}{}}}{\lx@inpgf@ignorespaces}{\lx@inpgf@ignorespaces}\hss}\lxSVG@discardpath\lxSVG@closescope \hss}}\lxSVG@closescope\endpgfpicture}}\pm 0.02$	$0.18\pm 0.16$
FM, DCC	$0.21\pm 0.05$	$\bf{0.05}\pm 0.03$	$0.27\pm 0.21$
FM, DCC, DrvEmb	$0.17\pm 0.05$	$0.10\pm 0.07$	$\hbox to21.78pt{\vbox to10.44pt{\pgfpicture\makeatletter\hbox{\hskip 10.88892pt\lower-5.22221pt\hbox to0.0pt{\lxSVG@begingroup@{_scopebegin=1} \lxSVG@begingroup@{stroke=#000000} \lxSVG@begingroup@{fill=#000000} \lxSVG@setlinewidth{\the\pgflinewidth}\lxSVG@begingroup@{stroke-width=0.4pt} \lx@inpgf@ignorespaces\nullfont\lxSVG@begingroup@{_scopebegin=1} \lxSVG@closescope \hbox to0.0pt{\lxSVG@begingroup@{_scopebegin=1} { {{}}\lx@inpgf@ignorespaces\hbox{\hbox{{\lxSVG@begingroup@{_scopebegin=1} \lxSVG@setlinewidth{\the\pgflinewidth}\lxSVG@begingroup@{stroke-width=0.4pt} \lx@inpgf@ignorespaces{{}{}{{ {}{}}}{ {}{}} {{}{{\lx@inpgf@ignorespaces}}}{{}{\lx@inpgf@ignorespaces}}{}{{}{\lx@inpgf@ignorespaces}} {\lxSVG@begingroup@{_scopebegin=1} \lxSVG@setlinewidth{\the\pgflinewidth}\lxSVG@begingroup@{stroke-width=0.4pt} \lx@inpgf@ignorespaces{}\lxSVG@stroke\lxSVG@drawpath@unclipped{M -14.79 -6.95 h 29.58 v 13.9 h -29.58 Z}{fill:none} \lx@inpgf@ignorespaces \lxSVG@closescope }{{{{\lx@inpgf@ignorespaces}}\lxSVG@begingroup@{_scopebegin=1} \lxSVG@transformcm{1.0}{0.0}{0.0}{1.0}{-8.88892pt}{-3.22221pt}\lxSVG@begingroup@{transform=matrix(1.0 0.0 0.0 1.0 -12.3 -4.46)} \pgfsys@hbox{58}\lxSVG@closescope }}} \lxSVG@closescope }}} } \lxSVG@closescope {{ {}{}{}}}{\lx@inpgf@ignorespaces}{\lx@inpgf@ignorespaces}\hss}\lxSVG@discardpath\lxSVG@closescope \hss}}\lxSVG@closescope\endpgfpicture}}\pm 0.06$
FM, CFG	$0.19\pm 0.04$	$0.07\pm 0.04$	$0.23\pm 0.15$
FM, CFG, DCC	$\bf{0.15}\pm 0.02$	$0.06\pm 0.02$	$0.18\pm 0.12$

TABLE I: Scenario-to-scenario distribution matching across drivers.

Model	$W_{2}^{\mathrm{norm}}$	$\Delta\mu^{\mathrm{norm}}$	$\\|\Delta\Sigma\\|_{F}^{\mathrm{norm}}$
Linear	$0.93\pm 0.00$	$0.98\pm 0.00$	$0.23\pm 0.00$
FM	$\bf{0.15}\pm 0.01$	$\hbox to21.78pt{\vbox to10.44pt{\pgfpicture\makeatletter\hbox{\hskip 10.88892pt\lower-5.22221pt\hbox to0.0pt{\lxSVG@begingroup@{_scopebegin=1} \lxSVG@begingroup@{stroke=#000000} \lxSVG@begingroup@{fill=#000000} \lxSVG@setlinewidth{\the\pgflinewidth}\lxSVG@begingroup@{stroke-width=0.4pt} \lx@inpgf@ignorespaces\nullfont\lxSVG@begingroup@{_scopebegin=1} \lxSVG@closescope \hbox to0.0pt{\lxSVG@begingroup@{_scopebegin=1} { {{}}\lx@inpgf@ignorespaces\hbox{\hbox{{\lxSVG@begingroup@{_scopebegin=1} \lxSVG@setlinewidth{\the\pgflinewidth}\lxSVG@begingroup@{stroke-width=0.4pt} \lx@inpgf@ignorespaces{{}{}{{ {}{}}}{ {}{}} {{}{{\lx@inpgf@ignorespaces}}}{{}{\lx@inpgf@ignorespaces}}{}{{}{\lx@inpgf@ignorespaces}} {\lxSVG@begingroup@{_scopebegin=1} \lxSVG@setlinewidth{\the\pgflinewidth}\lxSVG@begingroup@{stroke-width=0.4pt} \lx@inpgf@ignorespaces{}\lxSVG@stroke\lxSVG@drawpath@unclipped{M -14.79 -6.95 h 29.58 v 13.9 h -29.58 Z}{fill:none} \lx@inpgf@ignorespaces \lxSVG@closescope }{{{{\lx@inpgf@ignorespaces}}\lxSVG@begingroup@{_scopebegin=1} \lxSVG@transformcm{1.0}{0.0}{0.0}{1.0}{-8.88892pt}{-3.22221pt}\lxSVG@begingroup@{transform=matrix(1.0 0.0 0.0 1.0 -12.3 -4.46)} \pgfsys@hbox{58}\lxSVG@closescope }}} \lxSVG@closescope }}} } \lxSVG@closescope {{ {}{}{}}}{\lx@inpgf@ignorespaces}{\lx@inpgf@ignorespaces}\hss}\lxSVG@discardpath\lxSVG@closescope \hss}}\lxSVG@closescope\endpgfpicture}}\pm 0.03$	$0.24\pm 0.05$
FM, DCC	$0.16\pm 0.01$	$\bf{0.05}\pm 0.03$	$0.27\pm 0.05$
FM, DCC, DrvEmb	$0.16\pm 0.02$	$0.07\pm 0.03$	$0.24\pm 0.05$
FM, CFG	$0.17\pm 0.01$	$0.08\pm 0.03$	$\hbox to21.78pt{\vbox to10.44pt{\pgfpicture\makeatletter\hbox{\hskip 10.88892pt\lower-5.22221pt\hbox to0.0pt{\lxSVG@begingroup@{_scopebegin=1} \lxSVG@begingroup@{stroke=#000000} \lxSVG@begingroup@{fill=#000000} \lxSVG@setlinewidth{\the\pgflinewidth}\lxSVG@begingroup@{stroke-width=0.4pt} \lx@inpgf@ignorespaces\nullfont\lxSVG@begingroup@{_scopebegin=1} \lxSVG@closescope \hbox to0.0pt{\lxSVG@begingroup@{_scopebegin=1} { {{}}\lx@inpgf@ignorespaces\hbox{\hbox{{\lxSVG@begingroup@{_scopebegin=1} \lxSVG@setlinewidth{\the\pgflinewidth}\lxSVG@begingroup@{stroke-width=0.4pt} \lx@inpgf@ignorespaces{{}{}{{ {}{}}}{ {}{}} {{}{{\lx@inpgf@ignorespaces}}}{{}{\lx@inpgf@ignorespaces}}{}{{}{\lx@inpgf@ignorespaces}} {\lxSVG@begingroup@{_scopebegin=1} \lxSVG@setlinewidth{\the\pgflinewidth}\lxSVG@begingroup@{stroke-width=0.4pt} \lx@inpgf@ignorespaces{}\lxSVG@stroke\lxSVG@drawpath@unclipped{M -14.79 -6.95 h 29.58 v 13.9 h -29.58 Z}{fill:none} \lx@inpgf@ignorespaces \lxSVG@closescope }{{{{\lx@inpgf@ignorespaces}}\lxSVG@begingroup@{_scopebegin=1} \lxSVG@transformcm{1.0}{0.0}{0.0}{1.0}{-8.88892pt}{-3.22221pt}\lxSVG@begingroup@{transform=matrix(1.0 0.0 0.0 1.0 -12.3 -4.46)} \pgfsys@hbox{58}\lxSVG@closescope }}} \lxSVG@closescope }}} } \lxSVG@closescope {{ {}{}{}}}{\lx@inpgf@ignorespaces}{\lx@inpgf@ignorespaces}\hss}\lxSVG@discardpath\lxSVG@closescope \hss}}\lxSVG@closescope\endpgfpicture}}\pm 0.04$
FM, CFG, DCC	$0.27\pm 0.08$	$0.24\pm 0.11$	$\bf{0.18}\pm 0.09$

TABLE II: Scenario-to-scenario distribution matching for driver 5.

Model	$W_{2}^{\mathrm{norm}}$	$\Delta\mu^{\mathrm{norm}}$	$\\|\Delta\Sigma\\|_{F}^{\mathrm{norm}}$
Linear	$0.93\pm 0.00$	$0.98\pm 0.000$	$0.23\pm 0.00$
FM	$\hbox to21.78pt{\vbox to10.44pt{\pgfpicture\makeatletter\hbox{\hskip 10.88892pt\lower-5.22221pt\hbox to0.0pt{\lxSVG@begingroup@{_scopebegin=1} \lxSVG@begingroup@{stroke=#000000} \lxSVG@begingroup@{fill=#000000} \lxSVG@setlinewidth{\the\pgflinewidth}\lxSVG@begingroup@{stroke-width=0.4pt} \lx@inpgf@ignorespaces\nullfont\lxSVG@begingroup@{_scopebegin=1} \lxSVG@closescope \hbox to0.0pt{\lxSVG@begingroup@{_scopebegin=1} { {{}}\lx@inpgf@ignorespaces\hbox{\hbox{{\lxSVG@begingroup@{_scopebegin=1} \lxSVG@setlinewidth{\the\pgflinewidth}\lxSVG@begingroup@{stroke-width=0.4pt} \lx@inpgf@ignorespaces{{}{}{{ {}{}}}{ {}{}} {{}{{\lx@inpgf@ignorespaces}}}{{}{\lx@inpgf@ignorespaces}}{}{{}{\lx@inpgf@ignorespaces}} {\lxSVG@begingroup@{_scopebegin=1} \lxSVG@setlinewidth{\the\pgflinewidth}\lxSVG@begingroup@{stroke-width=0.4pt} \lx@inpgf@ignorespaces{}\lxSVG@stroke\lxSVG@drawpath@unclipped{M -14.79 -6.95 h 29.58 v 13.9 h -29.58 Z}{fill:none} \lx@inpgf@ignorespaces \lxSVG@closescope }{{{{\lx@inpgf@ignorespaces}}\lxSVG@begingroup@{_scopebegin=1} \lxSVG@transformcm{1.0}{0.0}{0.0}{1.0}{-8.88892pt}{-3.22221pt}\lxSVG@begingroup@{transform=matrix(1.0 0.0 0.0 1.0 -12.3 -4.46)} \pgfsys@hbox{58}\lxSVG@closescope }}} \lxSVG@closescope }}} } \lxSVG@closescope {{ {}{}{}}}{\lx@inpgf@ignorespaces}{\lx@inpgf@ignorespaces}\hss}\lxSVG@discardpath\lxSVG@closescope \hss}}\lxSVG@closescope\endpgfpicture}}\pm 0.02$	$\hbox to21.78pt{\vbox to10.44pt{\pgfpicture\makeatletter\hbox{\hskip 10.88892pt\lower-5.22221pt\hbox to0.0pt{\lxSVG@begingroup@{_scopebegin=1} \lxSVG@begingroup@{stroke=#000000} \lxSVG@begingroup@{fill=#000000} \lxSVG@setlinewidth{\the\pgflinewidth}\lxSVG@begingroup@{stroke-width=0.4pt} \lx@inpgf@ignorespaces\nullfont\lxSVG@begingroup@{_scopebegin=1} \lxSVG@closescope \hbox to0.0pt{\lxSVG@begingroup@{_scopebegin=1} { {{}}\lx@inpgf@ignorespaces\hbox{\hbox{{\lxSVG@begingroup@{_scopebegin=1} \lxSVG@setlinewidth{\the\pgflinewidth}\lxSVG@begingroup@{stroke-width=0.4pt} \lx@inpgf@ignorespaces{{}{}{{ {}{}}}{ {}{}} {{}{{\lx@inpgf@ignorespaces}}}{{}{\lx@inpgf@ignorespaces}}{}{{}{\lx@inpgf@ignorespaces}} {\lxSVG@begingroup@{_scopebegin=1} \lxSVG@setlinewidth{\the\pgflinewidth}\lxSVG@begingroup@{stroke-width=0.4pt} \lx@inpgf@ignorespaces{}\lxSVG@stroke\lxSVG@drawpath@unclipped{M -14.79 -6.95 h 29.58 v 13.9 h -29.58 Z}{fill:none} \lx@inpgf@ignorespaces \lxSVG@closescope }{{{{\lx@inpgf@ignorespaces}}\lxSVG@begingroup@{_scopebegin=1} \lxSVG@transformcm{1.0}{0.0}{0.0}{1.0}{-8.88892pt}{-3.22221pt}\lxSVG@begingroup@{transform=matrix(1.0 0.0 0.0 1.0 -12.3 -4.46)} \pgfsys@hbox{58}\lxSVG@closescope }}} \lxSVG@closescope }}} } \lxSVG@closescope {{ {}{}{}}}{\lx@inpgf@ignorespaces}{\lx@inpgf@ignorespaces}\hss}\lxSVG@discardpath\lxSVG@closescope \hss}}\lxSVG@closescope\endpgfpicture}}\pm 0.04$	$\hbox to21.78pt{\vbox to10.44pt{\pgfpicture\makeatletter\hbox{\hskip 10.88892pt\lower-5.22221pt\hbox to0.0pt{\lxSVG@begingroup@{_scopebegin=1} \lxSVG@begingroup@{stroke=#000000} \lxSVG@begingroup@{fill=#000000} \lxSVG@setlinewidth{\the\pgflinewidth}\lxSVG@begingroup@{stroke-width=0.4pt} \lx@inpgf@ignorespaces\nullfont\lxSVG@begingroup@{_scopebegin=1} \lxSVG@closescope \hbox to0.0pt{\lxSVG@begingroup@{_scopebegin=1} { {{}}\lx@inpgf@ignorespaces\hbox{\hbox{{\lxSVG@begingroup@{_scopebegin=1} \lxSVG@setlinewidth{\the\pgflinewidth}\lxSVG@begingroup@{stroke-width=0.4pt} \lx@inpgf@ignorespaces{{}{}{{ {}{}}}{ {}{}} {{}{{\lx@inpgf@ignorespaces}}}{{}{\lx@inpgf@ignorespaces}}{}{{}{\lx@inpgf@ignorespaces}} {\lxSVG@begingroup@{_scopebegin=1} \lxSVG@setlinewidth{\the\pgflinewidth}\lxSVG@begingroup@{stroke-width=0.4pt} \lx@inpgf@ignorespaces{}\lxSVG@stroke\lxSVG@drawpath@unclipped{M -14.79 -6.95 h 29.58 v 13.9 h -29.58 Z}{fill:none} \lx@inpgf@ignorespaces \lxSVG@closescope }{{{{\lx@inpgf@ignorespaces}}\lxSVG@begingroup@{_scopebegin=1} \lxSVG@transformcm{1.0}{0.0}{0.0}{1.0}{-8.88892pt}{-3.22221pt}\lxSVG@begingroup@{transform=matrix(1.0 0.0 0.0 1.0 -12.3 -4.46)} \pgfsys@hbox{58}\lxSVG@closescope }}} \lxSVG@closescope }}} } \lxSVG@closescope {{ {}{}{}}}{\lx@inpgf@ignorespaces}{\lx@inpgf@ignorespaces}\hss}\lxSVG@discardpath\lxSVG@closescope \hss}}\lxSVG@closescope\endpgfpicture}}\pm 0.06$
FM, DCC	$\bf{0.15}\pm 0.01$	$\bf{0.05}\pm 0.02$	$0.25\pm 0.05$
FM, CFG	$0.23\pm 0.05$	$0.18\pm 0.07$	$\bf{0.16}\pm 0.04$
FM, CFG, DCC	$0.50\pm 0.14$	$0.51\pm 0.17$	$0.27\pm 0.13$

TABLE III: Evaluation on Driver 5 held out during training.

Model	$W_{2}^{\mathrm{norm}}$	$\Delta\mu^{\mathrm{norm}}$	$\\|\Delta\Sigma\\|_{F}^{\mathrm{norm}}$
Linear	$1.46\pm 0.00$	$1.56\pm 0.00$	$0.13\pm 0.00$
FM	$0.71\pm 0.11$	$0.75\pm 0.11$	$0.09\pm 0.03$
FM with DCC	$\hbox to21.78pt{\vbox to10.44pt{\pgfpicture\makeatletter\hbox{\hskip 10.88892pt\lower-5.22221pt\hbox to0.0pt{\lxSVG@begingroup@{_scopebegin=1} \lxSVG@begingroup@{stroke=#000000} \lxSVG@begingroup@{fill=#000000} \lxSVG@setlinewidth{\the\pgflinewidth}\lxSVG@begingroup@{stroke-width=0.4pt} \lx@inpgf@ignorespaces\nullfont\lxSVG@begingroup@{_scopebegin=1} \lxSVG@closescope \hbox to0.0pt{\lxSVG@begingroup@{_scopebegin=1} { {{}}\lx@inpgf@ignorespaces\hbox{\hbox{{\lxSVG@begingroup@{_scopebegin=1} \lxSVG@setlinewidth{\the\pgflinewidth}\lxSVG@begingroup@{stroke-width=0.4pt} \lx@inpgf@ignorespaces{{}{}{{ {}{}}}{ {}{}} {{}{{\lx@inpgf@ignorespaces}}}{{}{\lx@inpgf@ignorespaces}}{}{{}{\lx@inpgf@ignorespaces}} {\lxSVG@begingroup@{_scopebegin=1} \lxSVG@setlinewidth{\the\pgflinewidth}\lxSVG@begingroup@{stroke-width=0.4pt} \lx@inpgf@ignorespaces{}\lxSVG@stroke\lxSVG@drawpath@unclipped{M -14.79 -6.95 h 29.58 v 13.9 h -29.58 Z}{fill:none} \lx@inpgf@ignorespaces \lxSVG@closescope }{{{{\lx@inpgf@ignorespaces}}\lxSVG@begingroup@{_scopebegin=1} \lxSVG@transformcm{1.0}{0.0}{0.0}{1.0}{-8.88892pt}{-3.22221pt}\lxSVG@begingroup@{transform=matrix(1.0 0.0 0.0 1.0 -12.3 -4.46)} \pgfsys@hbox{58}\lxSVG@closescope }}} \lxSVG@closescope }}} } \lxSVG@closescope {{ {}{}{}}}{\lx@inpgf@ignorespaces}{\lx@inpgf@ignorespaces}\hss}\lxSVG@discardpath\lxSVG@closescope \hss}}\lxSVG@closescope\endpgfpicture}}\pm 0.06$	$\hbox to21.78pt{\vbox to10.44pt{\pgfpicture\makeatletter\hbox{\hskip 10.88892pt\lower-5.22221pt\hbox to0.0pt{\lxSVG@begingroup@{_scopebegin=1} \lxSVG@begingroup@{stroke=#000000} \lxSVG@begingroup@{fill=#000000} \lxSVG@setlinewidth{\the\pgflinewidth}\lxSVG@begingroup@{stroke-width=0.4pt} \lx@inpgf@ignorespaces\nullfont\lxSVG@begingroup@{_scopebegin=1} \lxSVG@closescope \hbox to0.0pt{\lxSVG@begingroup@{_scopebegin=1} { {{}}\lx@inpgf@ignorespaces\hbox{\hbox{{\lxSVG@begingroup@{_scopebegin=1} \lxSVG@setlinewidth{\the\pgflinewidth}\lxSVG@begingroup@{stroke-width=0.4pt} \lx@inpgf@ignorespaces{{}{}{{ {}{}}}{ {}{}} {{}{{\lx@inpgf@ignorespaces}}}{{}{\lx@inpgf@ignorespaces}}{}{{}{\lx@inpgf@ignorespaces}} {\lxSVG@begingroup@{_scopebegin=1} \lxSVG@setlinewidth{\the\pgflinewidth}\lxSVG@begingroup@{stroke-width=0.4pt} \lx@inpgf@ignorespaces{}\lxSVG@stroke\lxSVG@drawpath@unclipped{M -14.79 -6.95 h 29.58 v 13.9 h -29.58 Z}{fill:none} \lx@inpgf@ignorespaces \lxSVG@closescope }{{{{\lx@inpgf@ignorespaces}}\lxSVG@begingroup@{_scopebegin=1} \lxSVG@transformcm{1.0}{0.0}{0.0}{1.0}{-8.88892pt}{-3.22221pt}\lxSVG@begingroup@{transform=matrix(1.0 0.0 0.0 1.0 -12.3 -4.46)} \pgfsys@hbox{58}\lxSVG@closescope }}} \lxSVG@closescope }}} } \lxSVG@closescope {{ {}{}{}}}{\lx@inpgf@ignorespaces}{\lx@inpgf@ignorespaces}\hss}\lxSVG@discardpath\lxSVG@closescope \hss}}\lxSVG@closescope\endpgfpicture}}\pm 0.06$	$0.08\pm 0.04$
FM with CFG	$\bf{0.60}\pm 0.09$	$\bf{0.64}\pm 0.09$	$\hbox to21.78pt{\vbox to10.44pt{\pgfpicture\makeatletter\hbox{\hskip 10.88892pt\lower-5.22221pt\hbox to0.0pt{\lxSVG@begingroup@{_scopebegin=1} \lxSVG@begingroup@{stroke=#000000} \lxSVG@begingroup@{fill=#000000} \lxSVG@setlinewidth{\the\pgflinewidth}\lxSVG@begingroup@{stroke-width=0.4pt} \lx@inpgf@ignorespaces\nullfont\lxSVG@begingroup@{_scopebegin=1} \lxSVG@closescope \hbox to0.0pt{\lxSVG@begingroup@{_scopebegin=1} { {{}}\lx@inpgf@ignorespaces\hbox{\hbox{{\lxSVG@begingroup@{_scopebegin=1} \lxSVG@setlinewidth{\the\pgflinewidth}\lxSVG@begingroup@{stroke-width=0.4pt} \lx@inpgf@ignorespaces{{}{}{{ {}{}}}{ {}{}} {{}{{\lx@inpgf@ignorespaces}}}{{}{\lx@inpgf@ignorespaces}}{}{{}{\lx@inpgf@ignorespaces}} {\lxSVG@begingroup@{_scopebegin=1} \lxSVG@setlinewidth{\the\pgflinewidth}\lxSVG@begingroup@{stroke-width=0.4pt} \lx@inpgf@ignorespaces{}\lxSVG@stroke\lxSVG@drawpath@unclipped{M -14.79 -6.95 h 29.58 v 13.9 h -29.58 Z}{fill:none} \lx@inpgf@ignorespaces \lxSVG@closescope }{{{{\lx@inpgf@ignorespaces}}\lxSVG@begingroup@{_scopebegin=1} \lxSVG@transformcm{1.0}{0.0}{0.0}{1.0}{-8.88892pt}{-3.22221pt}\lxSVG@begingroup@{transform=matrix(1.0 0.0 0.0 1.0 -12.3 -4.46)} \pgfsys@hbox{58}\lxSVG@closescope }}} \lxSVG@closescope }}} } \lxSVG@closescope {{ {}{}{}}}{\lx@inpgf@ignorespaces}{\lx@inpgf@ignorespaces}\hss}\lxSVG@discardpath\lxSVG@closescope \hss}}\lxSVG@closescope\endpgfpicture}}\pm 0.04$
FM with CFG, DCC	$0.76\pm 0.07$	$0.80\pm 0.08$	$\bf{0.06}\pm 0.02$

TABLE IV: Evaluation on Driver 4 held out during training.

Autonomous Driving

Autonomous driving develops vehicles that perceive road scenes, predict interactions, and plan and control safe movement with limited or no human input.

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Learning Direct Control Policies with Flow Matching for Autonomous Driving

Marcello Ceresini, Federico Pirazzoli, Andrea Bertogalli, Lorenzo Cipelli+4

1Università degli Studi di Parma · 2Alma Mater Studiorum - Università di Bologna · 3VisLab (an Ambarella Inc. company)

Flow Matching End-to-End Autonomous Driving OOD Generalization Autonomous Driving Data-Driven Control Autonomous Driving Planning

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We present a flow-matching planner for autonomous driving that directly outputs actionable control trajectories defined by acceleration and curvature profiles. The model is conditioned on a bird's-eye-view (BEV) raster of the surrounding scene and generates control sequences in a small number of Ordinary Differential Equations (ODE) integration steps, enabling low-latency inference suitable for real-time closed-loop re-planning. We train exclusively on urban scenarios (real urban city streets, intersections and roundabouts of the city of Parma, Italy) collected from a 2D traffic simulator with reactive agents, and evaluate in closed-loop on both in-distribution and markedly out-of-distribution environments, including multi-lane highways and unseen urban scenarios. Our results show that the model generalizes reliably to these unseen conditions, maintaining stable closed-loop control and successfully completing scenarios that differ substantially from the training distribution. We attribute this to the BEV representation, which provides a geometry-centric view of the scene that is inherently less sensitive to distributional shifts, and to the flow-matching formulation, which learns a smooth vector field that degrades gracefully under distribution shift. We provide video demonstrations of closed-loop behavior at https://marcelloceresini.github.io/DirectControlFlowMatching.

Abstract

Autonomous Driving

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