diff --git a/src/rs_distributions/transforms/fill_scale_tril.py b/src/rs_distributions/transforms/fill_scale_tril.py
index 03c97b4..f248f3f 100644
--- a/src/rs_distributions/transforms/fill_scale_tril.py
+++ b/src/rs_distributions/transforms/fill_scale_tril.py
@@ -5,6 +5,10 @@
 
 
 class FillTriL(Transform):
+    """
+    Transform for converting a real-valued vector into a lower triangular matrix
+    """
+
     def __init__(self):
         super().__init__()
 
@@ -21,16 +25,30 @@ def bijective(self):
         return True
 
     def _call(self, x):
+        """
+        Converts real-valued vector to lower triangular matrix.
+
+        Args:
+            x (torch.Tensor): input real-valued vector
+        Returns:
+            torch.Tensor: Lower triangular matrix
+        """
+
         return vec_to_tril_matrix(x)
 
     def _inverse(self, y):
         return tril_matrix_to_vec(y)
 
     def log_abs_det_jacobian(self, x, y):
-        return torch.zeros(x.shape[0], dtype=x.dtype, device=x.device)
+        batch_shape = x.shape[:-1]
+        return torch.zeros(batch_shape, dtype=x.dtype, device=x.device)
 
 
 class DiagTransform(Transform):
+    """
+    Applies transformation to the diagonal of a square matrix
+    """
+
     def __init__(self, diag_transform):
         super().__init__()
         self.diag_transform = diag_transform
@@ -48,10 +66,15 @@ def bijective(self):
         return self.diag_transform.bijective
 
     def _call(self, x):
+        """
+        Args:
+            x (torch.Tensor): Input matrix
+        Returns
+            torch.Tensor: Transformed matrix
+        """
         diagonal = x.diagonal(dim1=-2, dim2=-1)
         transformed_diagonal = self.diag_transform(diagonal)
-        shifted_diag = transformed_diagonal
-        result = x.diagonal_scatter(shifted_diag, dim1=-2, dim2=-1)
+        result = x.diagonal_scatter(transformed_diagonal, dim1=-2, dim2=-1)
 
         return result
 
@@ -66,9 +89,20 @@ def log_abs_det_jacobian(self, x, y):
 
 
 class FillScaleTriL(ComposeTransform):
+    """
+    A `ComposeTransform` that reshapes a real-valued vector into a lower triangular matrix.
+    The diagonal of the matrix is transformed with `diag_transform`.
+    """
+
     def __init__(self, diag_transform=SoftplusTransform()):
         super().__init__([FillTriL(), DiagTransform(diag_transform=diag_transform)])
+        self.diag_transform = diag_transform
 
     @property
     def bijective(self):
         return True
+
+    def log_abs_det_jacobian(self, x, y):
+        x = FillTriL()._call(x)
+        diagonal = x.diagonal(dim1=-2, dim2=-1)
+        return self.diag_transform.log_abs_det_jacobian(diagonal, diagonal)
diff --git a/tests/transforms/fill_scale_tril.py b/tests/transforms/fill_scale_tril.py
index 475960d..8d55a94 100644
--- a/tests/transforms/fill_scale_tril.py
+++ b/tests/transforms/fill_scale_tril.py
@@ -1,9 +1,12 @@
 import pytest
 from rs_distributions.transforms.fill_scale_tril import (
     FillScaleTriL,
+    FillTriL,
+    DiagTransform,
 )
 import torch
 from torch.distributions.constraints import lower_cholesky
+from torch.distributions.transforms import SoftplusTransform, ExpTransform
 
 
 @pytest.mark.parametrize("batch_shape, d", [((2, 3), 6), ((1, 4, 5), 10)])
@@ -35,3 +38,36 @@ def test_forward_equals_inverse(batch_shape, d):
     assert torch.allclose(
         input_vector, invL, atol=1e-4
     ), "Original input and the result of applying inverse transformation are not close enough"
+
+
+@pytest.mark.parametrize(
+    "batch_shape, d, diag_transform",
+    [
+        ((2, 3), 6, SoftplusTransform()),
+        ((1, 4, 5), 10, SoftplusTransform()),
+        ((2, 3), 6, ExpTransform()),
+        ((1, 4, 5), 10, ExpTransform()),
+    ],
+)
+def test_log_abs_det_jacobian_softplus_and_exp(batch_shape, d, diag_transform):
+    transform = FillScaleTriL(diag_transform=diag_transform)
+    input_shape = batch_shape + (d,)
+    input_vector = torch.randn(input_shape, requires_grad=True)
+    transformed_vector = transform(input_vector)
+
+    # Calculate log abs det jacobian with autograd
+    log_abs_det_jacobian = transform.log_abs_det_jacobian(
+        input_vector, transformed_vector
+    )
+
+    # Extract diagonal elements from input and transformed vectors
+    filltril = FillTriL()
+    diagtransform = DiagTransform(diag_transform=diag_transform)
+    tril = filltril(input_vector)
+    diagonal_transformed = diagtransform(tril)
+
+    # Calculate diagonal gradients with autograd
+    diag_jacobian = diagtransform.log_abs_det_jacobian(tril, diagonal_transformed)
+
+    # Assert diagonal gradients are approximately equal
+    assert torch.allclose(diag_jacobian, log_abs_det_jacobian, atol=1e-4)