diff --git a/src/brevitas/quant_tensor/__init__.py b/src/brevitas/quant_tensor/__init__.py
index d8bb253bb..bd1da8edd 100644
--- a/src/brevitas/quant_tensor/__init__.py
+++ b/src/brevitas/quant_tensor/__init__.py
@@ -15,6 +15,7 @@
 from .torch_handler import QUANT_TENSOR_FN_HANDLER
 
 IS_VALID_ATOL = 2e-1
+BFLOAT16_IS_VALID_ATOL = 0.5
 
 
 class QuantTensorBase(NamedTuple):
@@ -104,8 +105,15 @@ def is_not_none(self):
 
     @property
     def _pre_round_int_value(self):
-        int_value = self.value / self.scale
-        int_value = int_value + self.zero_point
+        value = self.value
+        scale = self.scale
+        zero_point = self.zero_point
+        if self.scale.dtype == torch.bfloat16:
+            value = self.value.type(torch.float32)
+            scale = self.scale.type(torch.float32)
+            zero_point = self.zero_point.type(torch.float32)
+        int_value = value / scale
+        int_value = int_value + zero_point
         return int_value
 
     @property
@@ -114,8 +122,9 @@ def is_valid(self):
             with torch.no_grad():
                 pre_round_int_value = self._pre_round_int_value
                 rounded_int_value = torch.round(pre_round_int_value)
-                is_int = torch.isclose(
-                    pre_round_int_value, rounded_int_value, atol=IS_VALID_ATOL).all()
+                max_abs_diff = torch.max(torch.abs(pre_round_int_value - rounded_int_value))
+                atol = BFLOAT16_IS_VALID_ATOL if self.value.dtype == torch.bfloat16 else IS_VALID_ATOL
+                is_int = max_abs_diff < atol
                 if self.bit_width >= 2:
                     if self.signed:
                         is_upper_b = (2.0 ** (self.bit_width - 1) - 1 >= rounded_int_value).all()
@@ -176,7 +185,12 @@ def int(self, float_datatype=False):
         if self.is_valid:
             int_value = round_ste(self._pre_round_int_value)
             if float_datatype:
-                return int_value
+                # Values at 8bit and lower can be represented exactly with float16 and bfloat16
+                # otherwise (e.g. Int16 bias), we upscale to float32
+                if self.bit_width <= 8.:
+                    return int_value.type(self.scale.dtype)
+                else:
+                    return int_value.type(torch.float32)
             else:
                 if self.bit_width <= 8. and self.signed_t.item():
                     return int_value.to(torch.int8)
@@ -301,6 +315,8 @@ def cat(tensors, dim, out=None):
 
     def __neg__(self):
         neg_value = (-self.int(float_datatype=True) - self.zero_point) * self.scale
+        # In case the dtype of self.int is different from the one of the scale
+        neg_value = neg_value.type(self.scale.dtype)
         if self.signed:
             return QuantTensor(
                 value=neg_value,
@@ -432,6 +448,8 @@ def __truediv__(self, other):
     def __abs__(self):
         if self.signed:
             abs_value = (torch.abs(self.int(float_datatype=True)) - self.zero_point) * self.scale
+            # In case the dtype of self.int is different from the one of the scale
+            abs_value = abs_value.type(self.scale.dtype)
             return QuantTensor(
                 value=abs_value,
                 scale=self.scale,