This is more of a sanity check question. Suppose I have a 512x512 image. I dispatch a down sampling compute shader with 256x256 threads total. I want to use hardware bilinear filtering, so for each thread with indices threadXY, I compute:

float2 uv = (threadXY*2 + 1) / 512;
float4 downsampledValue = tex.SampleLevel(linearSampler, uv, 0.0f);

I just want to make sure the +1 is correct, and not +0.5. The idea is if the image was 2x2, only one thread with indices (0,0) would get kicked off, and uv = (0.5, 0.5), which would be in the center of the 4 neighbor texels.

Yes, that's correct given the sizes you mentioned. The other way you an think about it (and what I would do personally, since I think it makes more sense) is compute your UV based on the output texel coordinate instead of the input texture. This would be uv = (threadXY + 0.5) / 256, since texel centers are located at 0.5. Doing it that way will make your shader work correctly even if the input size is not exactly 2x the output size.