We report the discovery of diffuse extended Ly α emission from redshift 3.1 to 4.5, tracing cosmic web filaments on scales of 2.5−4 cMpc. These structures have been observed in overdensities of Ly α emitters in the MUSE Extremely Deep Field, a 140 h deep MUSE observation located in the Hubble Ultra-Deep Field. Among the 22 overdense regions identified, five are likely to harbor very extended Ly α emission at high significance with an average surface brightness of 5 × 10 −20 erg s −1 cm −2 arcsec −2 . Remarkably, 70% of the total Ly α luminosity from these filaments comes from beyond the circumgalactic medium of any identified Ly α emitter. Fluorescent Ly α emission powered by the cosmic UV background can only account for less than 34% of this emission at z ≈ 3 and for not more than 10% at higher redshift. We find that the bulk of this diffuse emission can be reproduced by the unresolved Ly α emission of a large population of ultra low-luminosity Ly α emitters (< 10 40 erg s −1 ), provided that the faint end of the Ly α luminosity function is steep ( α ⪅ −1.8), it extends down to luminosities lower than 10 38 − 10 37 erg s −1 , and the clustering of these Ly α emitters is significant (filling factor < 1/6). If these Ly α emitters are powered by star formation, then this implies their luminosity function needs to extend down to star formation rates < 10 −4 M ⊙ yr −1 . These observations provide the first detection of the cosmic web in Ly α emission in typical filamentary environments and the first observational clue indicating the existence of a large population of ultra low-luminosity Ly α emitters at high redshift.