Many optoelectronic devices based on organic materials require rapid and long-range singlet exciton transport. Key factors that control the transport of singlet excitons includes the electronic structure of the material, disorder and exciton-phonon coupling. An important parameter whose influence on exciton transport has not been explored is the symmetry of the singlet electronic state (S1). Here, we employ femtosecond transient absorption spectroscopy and microscopy to reveal the relationship between the symmetry of S1 and exciton transport in highly aligned, near-disorder free, one-dimensional conjugated polymers based on polydiacetylene. By altering the torsional angle of the polymer backbone we control the symmetry of the S1 exciton and find that excitons with 2 1 Agsymmetry exhibit a significantly higher diffusion coefficient (34 ± 10 cm 2 s-1) compared to excitons with 1 1 Bu + symmetry (7 ± 6 cm 2 s-1). We also find that while exciton transport in the 2 1 A gstate occurs without exciton-exciton annihilation effects, 1 1 Bu + excitons undergo exciton-exciton annihilation. Both states are found to exhibit sub-diffusive behaviour, despite the large diffusion coefficient. Ab initio GW-BSE calculations reveal that this is due to the comparable strengths of the exciton-phonon interactionwhich tends to localise excitons, and the exciton couplingwhich tends to delocalise excitons. Our results demonstrate an intricate link between electronic state symmetry and exciton transport in π-conjugated polymer systems and also highlight the role of exciton-phonon coupling.