A preprint reports BFN-RL ahead of a matched categorical-diffusion system on Sokoban-7×7. BFN-RL recorded 68.7 ± 2.5% mean success, compared with 59.0 ± 2.6% for categorical diffusion. The authors report that BFN-RL was higher on all three training seeds, a 9.7-percentage-point improvement in mean success. But the wider discrete results were mixed: BFN-RL was competitive overall and did not uniformly outperform categorical diffusion. The manuscript is identified as arXiv:2608.25163v1 and dated 25 Aug 2026.
One planner, two kinds of state
BFN-RL is a Bayesian Flow Network sequence planner for both discrete and continuous domains. It models state sequences, conditions them on return, fixes the current state through inpainting and uses a second inverse-dynamics network to map consecutive states into actions. In practical terms, it generates a possible path through states and uses the action model to infer how that path could be followed.
The discrete experiments used 2,000 successful Empty-Random trajectories, 5,000 DoorKey trajectories, 3,000 BlockedUnlockPickup trajectories, 30,000 FrozenLake trajectories and 10,000 Sokoban trajectories.
The categorical-diffusion baseline was matched to BFN-RL on training data, temporal U-Net architecture, state representation, conditioning, current-state inpainting, inverse dynamics, planning horizon, action protocol and evaluation seeds. Discrete results were reported as mean ± sample standard deviation across three training seeds. Each seed was evaluated over 100 episodes, except FrozenLake, which used 200 episodes per seed.
Different grid worlds produced different leaders
On Empty-Random-6×6, categorical diffusion reported 100.0 ± 0.0% success and a 0.941 ± 0.012 mean return. BFN-RL reported 99.7 ± 0.6% success and a 0.895 ± 0.004 mean return. The paper also says categorical diffusion reached the goal more quickly.
DoorKey-8×8 shifted in the other direction. BFN-RL reported 100.0 ± 0.0% success and 0.934 ± 0.002 mean return, against 99.3 ± 0.6% success and 0.916 ± 0.010 mean return for categorical diffusion.
BlockedUnlockPickup again favored categorical diffusion. It reported 37.0 ± 13.5% success and 0.305 ± 0.113 mean return, compared with 32.7 ± 8.3% success and 0.279 ± 0.072 mean return for BFN-RL. The paper says variation between training seeds exceeded the difference in mean success on this task.
FrozenLake-8×8 was close. Categorical diffusion reported 85.5 ± 1.0% success, while BFN-RL reported 86.7 ± 1.3%. That gave BFN-RL the higher tabulated mean success, but the overall pattern still did not produce a uniform lead across the discrete tasks.
Continuous-control results were competitive
The same planner was also evaluated in continuous control. The authors describe BFN-RL's performance as comparable to the state of the art, using means and standard errors over three random seeds. The comparison has a qualification: every continuous-control value except BFN-RL came from an earlier cited study.
On the reported continuous-control average, BFN-RL scored 77.0, compared with 81.8 for DD and 75.3 for Diffuser. That put BFN-RL below DD and above Diffuser on the reported average.
A mixed benchmark picture
Taken together, BFN-RL offers a common planning framework for categorical and continuous domains, while the matched discrete comparison included tasks where each planner reported higher results. The continuous-control average placed BFN-RL between DD and Diffuser. The research received internal funding from the Norwegian University of Science and Technology.
Paper data and sources
Original title: Bayesian Flow Networks for Offline Trajectory Planning
Authors: Ludvig Killingberg, Helge Langseth
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-25
DOI: Not available
Original paper · Full text