Improving the PixelCNN with Discretized Logistic Mixture Likelihood and Other Modifications

## Improving the PixelCNN with Discretized Logistic Mixture Likelihood and Other Modifications

The PixelCNN is a powerful deep learning model that has been widely used for image generation and other tasks. However, the original PixelCNN suffers from some limitations, such as slow generation speed and difficulty in modeling complex distributions. To address these issues, researchers have proposed a modified version called PixelCNN++, which introduces several key improvements.

### Discretized Logistic Mixture Likelihood

One of the main limitations of the original PixelCNN is its use of a softmax output layer, which can struggle to model complex, multi-modal distributions. To overcome this, PixelCNN++ replaces the softmax with a discretized logistic mixture likelihood model.

The discretized logistic mixture likelihood is a flexible probability distribution that can capture a wide range of shapes and modes. It is defined as a mixture of K logistic distributions, each with its own mean, scale, and mixing coefficient. The model learns these parameters during training, allowing it to accurately represent the underlying distribution of the data.

This modification significantly improves the model’s ability to generate high-quality, diverse images, as it can better capture the complex patterns and structures present in natural images.

### Autoregressive Spatial Transformation

Another key innovation in PixelCNN++ is the introduction of autoregressive spatial transformations. In the original PixelCNN, the model generates pixels in a sequential, raster-scan order, which can lead to artifacts and inconsistencies in the generated images.

PixelCNN++ addresses this by incorporating a spatial transformation module that learns to warp the input image in an autoregressive manner. This allows the model to generate pixels in a more flexible, non-sequential order, which can lead to more coherent and visually appealing results.

The spatial transformation module is implemented using a convolutional neural network that predicts a set of transformation parameters for each pixel. These parameters are then used to warp the input image, and the transformed image is passed through the PixelCNN model to generate the output.

### Improved Conditioning

The original PixelCNN was limited in its ability to incorporate additional information, such as class labels or other conditioning variables, into the generation process. PixelCNN++ addresses this by introducing a more flexible conditioning mechanism.

Specifically, PixelCNN++ allows for the conditioning information to be injected at multiple stages of the model, including the initial input, the spatial transformation module, and the final output. This enables the model to more effectively leverage the available conditioning information, leading to improved generation quality and controllability.

### Faster Generation

One of the key limitations of the original PixelCNN was its slow generation speed, as it required sequentially generating each pixel in the output image. PixelCNN++ addresses this by introducing a parallel generation mechanism, which allows the model to generate all pixels simultaneously.

This is achieved by using a multi-scale architecture, where the model generates a coarse, low-resolution version of the image first, and then progressively refines it to produce the final high-resolution output. This approach significantly reduces the generation time, making PixelCNN++ a more practical choice for real-world applications.

### Improved Training and Sampling

PixelCNN++ also introduces several improvements to the training and sampling procedures, which can further enhance the model’s performance.

For example, the researchers propose using a multi-scale training regime, where the model is trained on images at different resolutions simultaneously. This can help the model learn more robust and generalizable features, leading to better generation quality.

Additionally, PixelCNN++ employs a more efficient sampling procedure that leverages the parallel generation capabilities of the model. This allows for faster and more diverse sample generation, making the model more suitable for applications that require rapid image synthesis.

Overall, the PixelCNN++ model represents a significant advancement in the field of image generation, addressing many of the limitations of the original PixelCNN and introducing a range of innovative techniques to improve the model’s performance and practicality.