What Is Left of the Pixel

The forward noising process has nothing to learn. Every step simply keeps a little less of the image and mixes in a little more fresh noise — a weighted average with a fixed recipe.

Here is a toy version of that recipe, acting on a single pixel. At every step the new value is

$x_t = 0.9\,x_{t-1} + 0.1\,n_t$

where $n_t$ is the fresh noise drawn at that step. A new number is drawn every step.

One pixel starts at $x_0 = 0.80$ . The forward process is run for two steps, and the noise it drew was

step $t$	noise $n_t$
1	$-0.50$
2	$1.20$

What is $x_2$ , the value of that pixel after the second step?

Round your answer to 3 decimal places.

What Is Left of the Pixel

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