Tomo­graph­ic Volu­met­ric Ad­dit­ive Man­u­fac­tur­ing (TVAM) is an emer­ging 3D print­ing tech­no­logy that can cre­ate com­plex ob­jects in un­der a minute. The key idea is to pro­ject in­tense light pat­terns onto a ro­tat­ing vi­al of photo-sens­it­ive res­in, caus­ing poly­mer­iz­a­tion where the cu­mu­lat­ive dose of these pat­terns reaches the poly­mer­iz­a­tion threshold. We for­mu­late the pat­tern cal­cu­la­tion as an in­verse light trans­port prob­lem and solve it via phys­ic­ally based dif­fer­en­ti­able ren­der­ing. In do­ing so, we ad­dress long-stand­ing lim­it­a­tions of pri­or work by ac­cur­ately mod­el­ing and cor­rect­ing for scat­ter­ing in com­pos­ite res­ins, print­ing in non-sym­met­ric vi­als, and sup­port­ing un­usu­al print­ing geo­met­ries. We also in­tro­duce an im­proved dis­cret­iz­a­tion scheme that ex­ploits the ray tra­cing op­er­a­tion to mit­ig­ate res­ol­u­tion-re­lated ar­ti­facts in prints. We demon­strate the be­ne­fits of our meth­od in real-world ex­per­i­ments, where our com­puted pat­terns pro­duce prints with an im­proved fi­del­ity.