Error Propagation in Keras DNN and/or CNN Regression - tensorflow

Question

Using Keras with Tensorflow as the backend, I have created both a CNN and DNN to predict three stellar parameters (Temperature, gravity, and metallicity) using the stellar spectra as an input. Both models predict very well when applied to test sets, but in order to make my results useful it is necessary to include errors in my predictions.
The input spectra each have 7000 data points and the output is 3 values. Each spectra also has an error array of 7000 data points that I would like to be able to propagate through my model so that there is a set of 3 uncertainties associated with each prediction. Does anyone have any experience or insight on how to accomplish this?
My DNN structure looks something like this:
# Define vars
activation = 'relu'
init = 'he_normal'
beta_1 = 0.9
beta_2 = 0.999
epsilon = 1e-08
input_shape = (None,7000)
epochs = 100
lr = 0.0009
batch_size = 64
n_hidden = [2048,1024,512,256,128]
# Design DNN Layers
model = Sequential([
InputLayer(batch_input_shape=input_shape),
Dense(n_hidden[0], init=init, activation=activation, bias=True),
Dense(n_hidden[1], init=init, activation=activation, bias=True),
Dense(n_hidden[2], init=init, activation=activation, bias=True),
Dense(n_hidden[3], init=init, activation=activation, bias=True),
Dense(n_hidden[4], init=init, activation=activation, bias=True),
Dense(l, init=init, activation='linear', bias=True),
])
# Optimization function
optimizer = Adam(lr=lr, beta_1=beta_1, beta_2=beta_2, epsilon=epsilon, decay=0.0)
# Compile and train network
model.compile(optimizer=optimizer, loss='mean_squared_error')
early_stopping = EarlyStopping(monitor='val_loss', min_delta=0.0001,
patience=3, verbose=2, mode='min')
## train_X.shape = (50000,7000)
## train_Y.shape = (50000,3)
## cv_X.shape = (10000,7000)
## cv_Y.shape = (10000,3)
history = model.fit(train_X, train_Y, validation_data=(cv_X, cv_Y),
nb_epoch=epochs, batch_size=batch_size, verbose=2, callbacks=[early_stopping])
My CNN is somewhat similar; basically replacing the first few layers with 1D-CNN layers and modifying the number of filters and filter lengths. Any thoughts on how to propagate errors through the model. I am familiar with some methods of obtaining the error of the model (through multiple trainings of the same model and/or dropout layers), but what I am looking for are errors in the actual predictions.
EDIT
Here is the architecture for my CNN
# Define vars
input_shape = (None,7000,1)
epochs = 30
activation = 'relu'
initializer = 'he_normal'
beta_1 = 0.9
beta_2 = 0.999
epsilon = 1e-08
batch_size = 64
n_hidden = [1024,512,256]
n_filters = [16,32,32,64,64]
lr = 0.001
model = Sequential([
InputLayer(batch_input_shape=input_shape),
Convolution1D(nb_filter=n_filters[0], filter_length=8, activation=activation, border_mode='same', init=initializer, input_shape=input_shape),
Convolution1D(nb_filter=n_filters[1], filter_length=8, activation=activation, border_mode='same', init=initializer),
MaxPooling1D(pool_length=4),
Convolution1D(nb_filter=n_filters[2], filter_length=8, activation=activation, border_mode='same', init=initializer),
Convolution1D(nb_filter=n_filters[3], filter_length=8, activation=activation, border_mode='same', init=initializer),
MaxPooling1D(pool_length=4),
Convolution1D(nb_filter=n_filters[4], filter_length=10, activation=activation),
MaxPooling1D(pool_length=4),
Flatten(),
Dense(output_dim=n_hidden[0], activation=activation, init=initializer),
Dense(output_dim=n_hidden[1], activation=activation, init=initializer),
Dense(output_dim=n_hidden[2], activation=activation, init=initializer),
Dense(output_dim=l, input_dim=n_hidden[2], activation='linear'),
])
# Compile Model
optimizer=Adam(lr=lr, beta_1=beta_1, beta_2=beta_2, epsilon=epsilon, decay=0.0)
model.compile(optimizer=optimizer, loss='mean_squared_error')
early_stopping = EarlyStopping(monitor='val_loss', min_delta=0.0001,
patience=3, verbose=2, mode='min')
history = model.fit(train_X, train_Y, validation_data=(cv_X, cv_Y),
nb_epoch=epochs, batch_size=batch_size, verbose=2, callbacks=[early_stopping])