Born in Lucerne, Diethelm studied at the Conservatory and the School of Church Music there (now both divisions of the Lucerne Musikhochschule). He studied composition privately with Johann Baptist Hilber (1891–1973) and Albert Jenny, and took master classes with Paul Hindemith and Arthur Honegger, which had a significant influence on him, in addition to summer courses in Darmstadt with Karlheinz Stockhausen and Luigi Nono. He completed his education as a conductor with Ernst Hans Beer and Alexander Krannhals.

Diethelm composed some 343 works in his lifetime, amongst them over 100 for full orchestra, chamber orchestra and string orchestra including eight symphonies, concertos for almost every instrument and a ballet; 40 works for choir with orchestra, instrumental ensemble or organ, including three oratorios and numerous cantatas; several works for a capella choir, including several masses and motets; more than 20 works for wind ensemble and brass band; and an extensive repertoire of chamber works ranging from solo instrumental pieces to nonettes and including six string quartets, solo sonatas for all instruments, 22 piano sonatas, and numerous works for unusual combinations of instruments.