What is the role of TimeDistributed layer in Keras?

I am trying to grasp what TimeDistributed wrapper does in Keras.

I get that TimeDistributed "applies a layer to every temporal slice of an input."

But I did some experiment and got the results that I cannot understand.

In short, in connection to LSTM layer, TimeDistributed and just Dense layer bear same results.

model = Sequential()
model.add(LSTM(5, input_shape = (10, 20), return_sequences = True))
model.add(TimeDistributed(Dense(1)))
print(model.output_shape)

model = Sequential()
model.add(LSTM(5, input_shape = (10, 20), return_sequences = True))
model.add((Dense(1)))
print(model.output_shape)

For both models, I got output shape of (None, 10, 1).

Can anyone explain the difference between TimeDistributed and Dense layer after an RNN layer?

In keras - while building a sequential model - usually the second dimension (one after sample dimension) - is related to a time dimension. This means that if for example, your data is 5-dim with (sample, time, width, length, channel) you could apply a convolutional layer using TimeDistributed (which is applicable to 4-dim with (sample, width, length, channel)) along a time dimension (applying the same layer to each time slice) in order to obtain 5-d output.

The case with Dense is that in keras from version 2.0 Dense is by default applied to only last dimension (e.g. if you apply Dense(10) to input with shape (n, m, o, p) you'll get output with shape (n, m, o, 10)) so in your case Dense and TimeDistributed(Dense) are equivalent.