Does matplotlib have a function for drawing diagonal lines in axis coordinates?

Drawing a diagonal from the lower left to the upper right corners of your plot would be accomplished by the following

ax.plot([0, 1], [0, 1], transform=ax.transAxes)

Using transform=ax.transAxes, the supplied x and y coordinates are interpreted as axes coordinates instead of data coordinates.

This, as @fqq pointed out, is only the identity line when your x and y limits are equal. To draw the line y=x such that it always extends to the limits of your plot, an approach similar to the one given by @Ffisegydd would work, and can be written as the following function.

def add_identity(axes, *line_args, **line_kwargs):
    identity, = axes.plot([], [], *line_args, **line_kwargs)
    def callback(axes):
        low_x, high_x = axes.get_xlim()
        low_y, high_y = axes.get_ylim()
        low = max(low_x, low_y)
        high = min(high_x, high_y)
        identity.set_data([low, high], [low, high])
    callback(axes)
    axes.callbacks.connect('xlim_changed', callback)
    axes.callbacks.connect('ylim_changed', callback)
    return axes

Example usage:

import numpy as np
import matplotlib.pyplot as plt

mean, cov = [0, 0], [(1, .6), (.6, 1)]
x, y = np.random.multivariate_normal(mean, cov, 100).T
y += x + 1

f, ax = plt.subplots(figsize=(6, 6))
ax.scatter(x, y, c=".3")
add_identity(ax, color="r", ls="--")

plt.show()