Well as it stands that would make the diplomacy techs better for culture than the culture techs themselves.

That was the point, you're really better off just buffing the existing tech first.

The real problem with culture isn't with the techs IMO- it's the game constants.  Most specifically it's too easy to defend against culture with friendly culture.  You can easily have twice the culture rate of an adjacent enemy world and not even have your culture on their doorstep.

More to the point, early game when players are likely to only have 1-2 culture buildings tops on a given front, the culture techs are more or less unnoticeable at this stage of the game- +10-20% culture rate isn't going to change the fact that your 1-2 culture buildings aren't going to come anywhere near overpowering the enemy's 1 culture buildings.

A player with more culture buildings on the border(even if only slightly more) and superior culture techs should IMO have no problem causing allegiance loss.   Getting the ball rolling on allegiance loss shouldn't be as hard as it is now- after all the opponents have a long reaction time to build more culture buildings or send in capitalships before they actually lose the planet  and consequently keeping that proverbial ball rolling is hard in it's self.

But then, it's likely too late in beta to start with sweeping changes to core game mechanics like culture.

Yesterday i played a game with hard TEC in my Solar system.
I was Advent Loyayl, full tech into culture. Some of my key planets had a culture rate over 40.
And the TEC with no culture centers on the nearby planets, only a few centers maybe 2 jumps away from it...i could not reach the planet with my culture. I dont know what went wrong there.

In my opinion the culture is fine as it is now.
If you could set it to different targets (maybe planet based) it would be also a very nice idea, specially for players who wants to overwhelm enemy planets by culture, not by military.

But i think Diplomacy should not affect the Culture.
All factions have different Culture research things in the civillian trees, it is enough i think.
That you cant stand so well against a full teched Advent Loyalist is also fine, i mean...our ships are paperplanes with lasers

Unfortunately most see culture as an afterthought. A slight economic boost or an annoying poke to research a broadcast/communion tower to make someone else's go away.

But that is actually an "economic" research, so the research choice for a player will be: military / economy / slight military + slight economy.

And what I want is: military / economy / culture. Make the culture transmission bonus from research something more serious, so that if a player choose to research it instead of damage or resource bonus, it will be really useful to help to convert planets of his rivals, but not a suicide behavior.

what I would do is make your capital planet always generate culture, even before you researched anything in it. Research only makes culture better and allows construction of culture centers. Putting it out there right away helps make it more important in the early game, but not something you have to invest in either.

Next, Allegiance is only gained through culture. This makes culture much more important at all times. uncultured planets should still be colonizable, but will start at some allegiance and fall off until culture is there

Last, some number adjustments based off play testing. Maybe the spread rate loss per branch would have to be toned down or something. I would see quick spreading culture as not a big problem, but the key difference between a culture oriented player and one who isn't would be the research each has into cultural resistance or the pressure against an opposing culture (look, I know not everyone has the same modifiers, but I'm not sure which)