a beautiful feeling that is a result of suffering

Your description brings to mind the words "glory" and "glorious", which can be defined as a "profound expression of beauty". As beauty, it can be perceived in many ways - not only visually. It certainly encompasses the concept of victory - "derived from overcoming obstacles, pain, and sufferings". It seems similar to "Yugen" as an obviously present, but inexpressible beauty.

Glory - The Free Dictionary

Glorious - The Free Dictionary

Disclaimer: I don't know japanese.

In support of user22542's answer, here is a poem which answers what I have understood of your concept (from what little grief I have known; however it may compare to your own experience, I have suffered very little physical torture):

Defeat may serve as well as victory
To shake the soul and let the glory out.
When the great oak is straining in the wind
The boughs drink in new beauty and the trunk
Sends down a deeper root on the windward side.
Only the soul that knows the mighty grief
Can know the mighty rapture. Sorrows come
To stretch out spaces in the heart for joy.
– Edwin Markham (1852-1940), emphasis added.

"Annealed" is sometimes used in the sense you're describing.

The years he spent in prison annealed his spirit.

1. (Metallurgy) to temper or toughen (something) by heat treatment
2. (General Physics) to subject to or undergo some physical treatment, esp heating, that removes internal stress, crystal defects, and dislocations
3. (tr) to toughen or strengthen (the will, determination, etc)
4. (General Physics) (often foll by out) physics to disappear or cause to disappear by a rearrangement of atoms: defects anneal out at different temperatures. https://www.thefreedictionary.com/annealed