What is the diffusion in judaism?

Answer 1

Using the word "diffusion" makes it unclear what you're asking. There are at least two kinds of diffusion in Judaism: what types of Jews there are, and where Jews are located in the scattering of the Diaspora.

1) Types of Jews:

Jews may be classed according to lifestyle, geography, or outlook.
Lifestyle: there are Jews who are more stringent (Orthodox) or less stringent (Conservative, Reform) in their observance of the Torah's commands.
Geography: there are Ashkenazi (Western) Jews and Sephardi/Mizrahi (Eastern) Jews. Ashkenazim have historical roots in Germany, while Sephardim have historical roots in pre-expulsion Spain. (There are others too, such as Yemeni, Romaniote, and Persian Jews, but the above are the largest groups.)
Outlook: among the religious Jewish communities, there are the Yeshiva community, Hassidim, and Modern Orthodox. (Hassidim are the ones who wear long frock-coats.)

2) Where Jews are:

The Diaspora (scattering of the Jewish people) began because we were unable to live in the Holy Land.
A) Around 2600 years ago, the Assyrians forcibly exiled the Ten Israelite tribes to points unknown. A small percentage of each of these tribes is still among us, but most of them were exiled.
B) Around 2500 years ago, the Babylonians destroyed the First Temple and forcibly exiled the remainder of Israel's population to Babylonia.
While the Jews were permitted to return to Israel (Judea) seventy years later, and tens of thousands did so (and rebuilt the Temple), most of them remained in Babylonia, while others began to settle in North Africa, southern Europe, the Crimea, throughout the Near East and elsewhere.
C) In 68 CE, the Romans destroyed the Second Temple. The Romans did not force the Jews out of Judea in a single expulsion. Rather, the Romans expelled them from Jerusalem only; and the rest of Judea lost its Jews slowly, over a period of centuries, as conditions in Judea became too harsh. Even then, we have records of Jewish communities who lived in Judea (Palestine) during the entire period of the last two millenia.
Those Jews who left Judea went to southern Europe, North Africa, Arabia, the Near East, and (slowly) further afield (especially throughout Europe).

The Jews today (2014):

Israel.......... 6,110,000
America....... 5,425,000
France......... 478,000
Canada........ 380,000
United Kingdom 290,000
Russia........ 190,000
Argentina.... 181,500
Germany......118,000
Brazil........... 107,300
Australia...... 97,500
South Africa.. 70,000
Ukraine......... 65,000
Hungary........ 48,000
Mexico.......... 40,000
Belgium........ 30,000
Holland......... 29,900
Italy.............. 28,100
Chile............. 18,500
Other countries, combined: 250,200.