State-of-the-art dens­ity es­tim­a­tion meth­ods for ren­der­ing par­ti­cip­at­ing me­dia rely on a dense photon rep­res­ent­a­tion of the ra­di­ance dis­tri­bu­tion with­in a scene. A crit­ic­al bot­tle­neck of such ker­nel-based ap­proaches is the ex­cess­ive num­ber of photons that are re­quired in prac­tice to re­solve fine il­lu­min­a­tion de­tails, while con­trolling the amount of noise. In this pa­per, we pro­pose a para­met­ric dens­ity es­tim­a­tion tech­nique that rep­res­ents ra­di­ance us­ing a hier­arch­ic­al Gaus­si­an mix­ture. We ef­fi­ciently ob­tain the coef­fi­cients of this mix­ture us­ing a pro­gress­ive and ac­cel­er­ated form of the Ex­pect­a­tion-Max­im­iz­a­tion al­gorithm. After this step, we are able to cre­ate noise-free ren­der­ings of high-fre­quency il­lu­min­a­tion us­ing only a few thou­sand Gaus­si­an terms, where mil­lions of photons are tra­di­tion­ally re­quired. Tem­por­al co­her­ence is trivi­ally sup­por­ted with­in this frame­work, and the com­pact foot­print is also use­ful in the con­text of real-time visu­al­iz­a­tion. We demon­strate a hier­arch­ic­al ray tra­cing-based im­ple­ment­a­tion, as well as a fast splat­ting ap­proach that can in­ter­act­ively render an­im­ated volume caustics.