Which Google Cloud Platform service is the easiest for running Tensorflow?

Summing up the answers:

• AI Platform Notebooks - One click Jupyter Lab environment
• Deep Learning VMs images - Raw VMs with ML libraries pre-installed
• Deep Learning Container Images - Containerized versions of the DLVM images
• Cloud ML
• Manual installation on Compute Engine. See instructions below.

Instructions to manually run TensorFlow on Compute Engine:

1. Create a project
2. Open the Cloud Shell (a button at the top)
3. List machine types: gcloud compute machine-types list. You can change the machine type I used in the next command.
4. Create an instance:

gcloud compute instances create tf \
  --image container-vm \
  --zone europe-west1-c \
  --machine-type n1-standard-2

4. Run sudo docker run -d -p 8888:8888 --name tf b.gcr.io/tensorflow-udacity/assignments:0.5.0 (change the image name to the desired one)
5. Find your instance in the dashboard and edit default network.
6. Add a firewall rule to allow your IP as well as protocol and port tcp:8888.
7. Find the External IP of the instance from the dashboard. Open IP:8888 on your browser. Done!
8. When you are finished, delete the created cluster to avoid charges.

This is how I did it and it worked. I am sure there is an easier way to do it.

More Resources

You might be interested to learn more about:

• Google Cloud Shell
• Container-Optimized Google Compute Engine Images
• Google Cloud SDK for a more responsive shell and more.

Good to know

• "The contents of your Cloud Shell home directory persist across projects between all Cloud Shell sessions, even after the virtual machine terminates and is restarted"
• To list all available image versions: gcloud compute images list --project google-containers

Thanks to @user728291, @MattW, @CJCullen, and @zain-rizvi

Google Cloud Machine Learning is open to the world in Beta form today. It provides TensorFlow as a Service so you don't have to manage machines and other raw resources. As part of the Beta release, Datalab has been updated to provide commands and utilities for machine learning. Check it out at: http://cloud.google.com/ml.