that is not a breather hose but a PCV hose (positive crankcase ventilation) meron dyan oil due to "oil mist" during engine operation, although meron yan oil separator sa loob ng valve cover, still its not sufficient to perfectly separate the oil mixed with air... meron din smoke dyan since your engine blowby hose is tapped to the valve cover then yung PCV hose papunta sa intake to recirculate the blowby gases past the piston rings and valves to the combustion chamber...

yung mga unang diesel engine meron sila draft tube, yung nakalaylay lang, dati kasi ok lang na ganun ang setup pero modern emission controls, pinagbawal na yung ganung system so pinasok nila sa engine valve cover to recirculate the blowby gases.. normal lang na may usok dyan kasi diesel engines normally have blowby talaga considering na diesel engines operate under high compression to burn fuel...

pwede mo din ilagay yan sa baba ng engine pero may oil na tutulo dyan gawa nung oil mist, pwede mo din lagyan ng oil collector para hindi magkalat ng langis..

btw, even gas engines have that PCV hose, although hindi mo mapapansin na may smoke kasi gas engine nga, pero may oil din na makukuha yung engine kaya minsan nasisira yung mga sensor sa intake lalo na kung EFI..