Sauce Diane is not the same as the sauce that is produced in making Steak Diane.
Larousse Gastronomique (1988 edition) refers to it as a cream sauce flavoured with peppercorns and truffles.
Escoffier in his Guide Culinaire, 1907, calls for cream, Sauce Poivrade, truffle, hard-boiled egg white, and says the sauce is for venison.
In his 1894 book called “The Epicurean”, Charles Ranhofer, the Delmonico chef, gives a more detailed though quite different account of what a Sauce Diane is. Bearing in mind that the Diane in question is, after all, the Greek goddess of the hunt, it could be argued that his version is the truest to overall definition of “Diane”, in that his sauce not only is for game, but actualy contains game.
He calls for finely minced onion, shallots and celery to be sautéed a bit in butter with a bay leaf. A small game bird carcass is added and browned, then a roux is made by adding flour around the carcass, stirring it into the veg, and cooking until the roux is golden. Then, equal amounts of velouté stock and cream are added, and the entire mixture simmered for half an hour. The sauce is then seasoned, then strained to remove all the solid ingredients, then simmered more to reduce it, then finished with butter.
Literature & Lore
(460). DIANA SAUCE (Sauce à la Diane). Into a saucepan put a quarter of a pound of butter; when hot add to it one medium onion, two shallots, one ounce of celery, all cut up very finely, and a bay leaf, and when these ingredients are well fried, add to them one pound of raw game carcass, and let the whole color nicely, adding three tablespoonfuls of flour, to make a roux, brown it slightly and then moisten with one pint of velouté stock (No. 422) and a pint of cream. Let the sauce cook and despumate [Ed.: sic] for half an hour, seasoning it with salt, pepper, and nutmeg; then strain it through a sieve, and afterward through a tammy [Ed.: strainer], return it to the saucepan, and reduce it properly, incorporating into it two ounces of butter.
— Ranhofer, Charles. The Epicurean. A Complete Treatise of Analytical and Practical Studies on The Culinary Art . Ranhofer. 1894. Page 303.