Fully visible belief network (FVBN)

Explicit density model

• $p(x)$ = likelihood of image x
• $p(x_1,x_2,...,x_n)$ = joint likelihood of each pixel in the image
  Use chain rule to decompose likelihood of an image x into product of 1-d distributions
  
  Then, maximize likelihood of training data

PixelRNN

1. Generate image pixels one at a time, starting at the upper left corner
2. Compute a hidden state for each pixel that depends on hidden states and RGB values from the left and from above
3. At each pixel, predict red, then blue, then green
   1. Softmax over [0, 1, …, 255]

Each pixel depends implicitly on all pixels above and to the left

PixelCNN

1. Still generate image pixels starting from corner
2. Dependency on previous pixels now modelled using a CNN over context region (masked convolution)
   Training faster than PixelRNN
   Generation still sequential → slow
   

Improving PixelCNN performance

• Gated convolutional layers
• Short-cut connections
• Discretized logistic loss
• Multi-scale
• Training tricks
• Etc…