Unexpected behavior from tfd.MarkovChain sample method

Can someone help to explain why the MarkovChain does not generate independent samples after using a bijector in the transition_fn? Thanks!!!

In the codes below, gaussian_walk1 and gaussian_walk2 are expected to be the same, since normal(x,1)=x+normal(0,1). While gaussian_walk1.sample(5) gives expected independent samples, gaussian_walk2.sample(5) gives identical samples.

gaussian_walk1 = tfd.MarkovChain(
 initial_state_prior=tfp.distributions.Deterministic(0.),
 transition_fn=lambda _, x: tfd.Normal(loc=x, scale=1.),
 num_steps=10)

gaussian_walk2 = tfd.MarkovChain(
 initial_state_prior=tfp.distributions.Deterministic(0.),
 transition_fn=lambda _, x: tfd.TransformedDistribution(distribution=tfd.Normal(loc=0.0, scale=1.),bijector=tfp.bijectors.Shift(x)),
 num_steps=10)

gaussian_walk1.sample(5)

<tf.Tensor: shape=(5, 10), dtype=float32, numpy=
array([[ 0.        ,  0.4963878 ,  0.0830816 , -0.77141273, -0.91577226,
         0.23975712,  0.49968088, -2.0648232 , -2.0975184 , -3.7448356 ],
       [ 0.        , -2.2646387 , -0.8099165 , -1.6681502 , -1.4593805 ,
        -1.5122384 , -1.7060741 , -1.7010493 , -0.828577  , -1.4167368 ],
       [ 0.        ,  0.06805495, -0.32092297, -1.0535722 , -2.30161   ,
        -3.9674587 , -4.319279  , -4.5414166 , -3.836207  , -4.32444   ],
       [ 0.        ,  2.509243  ,  3.1126018 ,  3.8786044 ,  5.56534   ,
         6.333398  ,  6.178385  ,  5.152129  ,  4.0463457 ,  4.3648543 ],
       [ 0.        ,  0.3113255 ,  0.9251684 ,  0.81194293,  0.48614424,
         0.05987284, -1.2350528 , -0.2448535 ,  0.2054899 ,  0.6470542 ]],
      dtype=float32)>

gaussian_walk2.sample(5)

<tf.Tensor: shape=(5, 10), dtype=float32, numpy=
array([[ 0.        , -0.655154  , -0.19072625, -0.9975474 , -0.86116153,
        -1.215732  , -1.2559065 , -1.4174258 ,  0.42590857, -0.99431324],
       [ 0.        , -0.655154  , -0.19072625, -0.9975474 , -0.86116153,
        -1.215732  , -1.2559065 , -1.4174258 ,  0.42590857, -0.99431324],
       [ 0.        , -0.655154  , -0.19072625, -0.9975474 , -0.86116153,
        -1.215732  , -1.2559065 , -1.4174258 ,  0.42590857, -0.99431324],
       [ 0.        , -0.655154  , -0.19072625, -0.9975474 , -0.86116153,
        -1.215732  , -1.2559065 , -1.4174258 ,  0.42590857, -0.99431324],
       [ 0.        , -0.655154  , -0.19072625, -0.9975474 , -0.86116153,
        -1.215732  , -1.2559065 , -1.4174258 ,  0.42590857, -0.99431324]],
      dtype=float32)>

No source files or tests are named. Reproduce the two snippets, then trace MarkovChain.sample together with TransformedDistribution and the Shift bijector to compare their sampling paths. Done means the cause of the identical samples is established and documented, with a focused regression test or fix if the behavior is confirmed as a defect.