There's nothing making gaseous diffusion more efficient than 1940s centrifuge separation. Just because the US program considered it less efficient/not worth pursuing doesn't mean that the European/Asian programs thought the same.
The German program pursued the centrifuge method from the beginning and the Japanese from late 44/early 45 because they considered it more efficient and simpler to build.
And even if the Soviets make a less efficient centrifuge than gaseous diffusion, so what? They will still get a bomb at the price of an extra tone of uranium.
And the Soviets still ended up building big gaseous diffusion plants despite their scientists not likeing the route. They would not have spent the money if they had an equally efficient centrifuge route available, they would have cancelled it like they did electromagnetic separation, where they improved on the US process but still was not as efficient
Both of those programs were basically pure experimental, so they may have thought for the quantities they needed
The so what is that it takes them longer to get enough enriched material to do the experimental work to do the engineering work to get the bomb, and slightly longer to get the bomb. I've never said they won't, I just figure 2-3 years more time to account for less efficient production and doing more trial and error
Their grasp on the theory was firmly solid and well understood by 1944, and by 1945 they were already looking into fission boosted bombs with tritium or lithium deuterite so I would say the German had it covered, as for the Japanese, by 1945 they also understood how a U-233/U-235 bomb would work.
I've heard completely differently about both programs and that the Farm Hall transcripts pretty much indicate Germany had no functional bomb program and didn't even have a good critical mass calculation. They may have known "large amount of highly enriched Uranium/plutonium, compression, boom" but I haven't seen indications they knew enough to calculate a critical mass given all the interacting factors involved and that some of their fundamental calculations were pretty off(IE neutron absorption of Graphite)
The Germans did touch the engineering aspects though, the most visible aspect being their thousand or so uranium metal cubes for their reactors, other less visible aspects being a heavy water plant, the manufacturing of centrifuges in Kiel, building of cyclotrons, experiments with explosive lens etc. I don't know enough about the engineering aspects of the Japanese program to comment.
The Japanese were still purely in the experimental phase. The Germans were working on some of the issues but they didn't get particularly far, they could make cubes of Uranium Oxide but hadn't really worked on the pure metal itself and hadn't touched Plutonium, they didn't really work on the fusing issue, they hadn't solved one of the biggest issues with Centrifuges that the US did, how far they got in explosive lenses is a question
Not sure about a smaller budget, it was the highest priority program in the Soviet Union and had no lack of funding throughout its life.
While the highest priority program for the Soviet Union, it is still a program from a war ravaged state that was substantially poorer than the US before losing 30 million people and having its industrial regions wrecked by the war, and in 1946 is in a borderline state of famine. Quite simply put it won't have the same resources as the top priority program from a richer state