The interpolation used to upsample/downsample the image

[KevinWang676]

Hi, I'm trying to understand the math part of your algorithm. And I wonder which interpolation you use in order to upsample/downsample the image. I saw both LANCZOS and BILINEAR interpolation in function.py, so I'm a little confused. Could you explain how you use these two interpolations? Thank you in advance.

[fallenshock]

Hi, we use LANCZOS to create the downsampled versions of the image, and BILINEAR to create their blurry upsampled versions for training. We use the same bilinear interpolation during upsampling in the sampling process.

[KevinWang676]

Hi, thanks for you reply! It helps a lot. I have another question on the math part.

• Do you have an exact formula for the relationship between $x_{t}^{s}$ and $x_{t-1}^{s}$?

Because in your paper there is only the relationship between $x_{t}^{s}$ and $x_{t}^{s, \text{mix}}$ as shown below

$x_{t}^{s} = \sqrt{\bar{\alpha}_t} x_{t}^{s, \text{mix}} + \sqrt{1-\bar{\alpha}_t} \epsilon$