Hello,
I have improved the colors of a firework on RawTherapee and I reduced the noise but when I saved the picture and I looked at it, the noise came back (in the smoke below the firework).
I tried different formats (jpeg, tiff, png) but it doesn’t work and that degrades the image.
How to avoid seeing the noise on the final picture ??
@valentine_bokeh Welcome to the forum!
When I zoom in, it doesn’t look like noise but compression (or gamut) artifacts. What are your export settings? Are they at max quality?
There are also some some Hot/Dead pixel which can be removed with the Hot/Dead pixel tool.
Yes I have tried all formats but the best (tiff 32-bit float) degrades the quality.
When I zoom the picture on RawTherapee, the noise disappears but when I save all the picture it’s there 
You might want to try the dev releases[1]. Note that the pp3s aren’t backwards compatible. I recall there being an issue at one point that was discussed here in the forums. Try searching for it.
As already said, it doesn’t look like noise.
Could be a color space conversion issue ? For example if you work in Prophoto while you export in sRGB.
Try to remain in the same color space. sRGB profile for both: workspace and export.
This is only acceptable if sRGB will be your only color space.
I agree, I only suggested a test to search for a reason of the difference between output file and what is displayed in RT.
Welcome @valentine_bokeh
If you accept to upload the raw file and the pp3 (with license CC BY-SA), I think people could provide more precise and relevant advice.
Use filebin or equivalent and post the link here.
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Maybe the problem is the file isn’t a raw…
That can explain the problem.
Nevertheless, it could be interesting to see what happens if you upload your photo.