Stable Diffusion

Civitai has a bunch of Lora's that might help with crispness? My favourites are Denoise & AddDetail. I'd also use a popular SD1.5 model like Deliberate (until sdxl is released). I always do highres fix, maybe scale 2x from 512 on a low denoise & see what you think.

There's also an after detailer extension I use for doing extra processing passes on hands/face etc.

Honestly I go through a process where I place the image into img to img and re-render the image at increasingly lower and lower denoising scales until I get a result that looks good. I tend to alternate between sampling models too, depending on what I'm going for. Haven't quite got the hang of inpainting yet, but I've seen other people's workflows of upscaling the image and then address problem areas individually.

You mean the step after the ludicrous amount of inpainting one has to do sometimes?

Apart from the mentioned adddetail lora (works in negative prompt as well), maybe rerunning the image through ultimate sd upscaler with the controlnet extension? (go easy on the denoise level here, or your image becomes a surrealist's dream)

I use SD to make character portraits for TTRPGs online and I’ve had decent luck fixing images with Photoshop (Beta) generative fill. It’s good at some things, like replacing one eye so that it better matches the other. It’s okay at noses. It’s very bad at mouths. It’s good at removing backgrounds or replacing something with background. Extending images is 50-50 but it can be nice for getting a character centred in frame, or for filling in the top of their head if it was cut off. It’s also pretty good at blending two images- for example, I often have a good full body image with a really weird face; it makes it a lot easier to paste a different face on top and blend the edges.

I know this is a paid option for what you’re asking but hopefully it helps.