diff --git a/timm/optim/adafactor_bv.py b/timm/optim/adafactor_bv.py
index ea8a4afa..d603b528 100644
--- a/timm/optim/adafactor_bv.py
+++ b/timm/optim/adafactor_bv.py
@@ -51,7 +51,7 @@ class AdafactorBigVision(Optimizer):
             beta2_cap: float = 0.999,
             momentum: Optional[float] = 0.9,
             momentum_dtype: Union[str, torch.dtype] = torch.bfloat16,
-            eps: float = 1e-30,
+            eps: Optional[float] = None,
             weight_decay: float = 0.0,
             clipping_threshold: Optional[float] = None,
             unscaled_wd: bool = False,
@@ -66,6 +66,7 @@ class AdafactorBigVision(Optimizer):
             else:
                 assert momentum_dtype == 'float32', f'{momentum_dtype} dtype not supported'
                 momentum_dtype = torch.float32
+        # FIXME try to check if momentum dtype is appropriate for device? Torch API not great for this.
 
         defaults = dict(
             lr=lr,
@@ -212,6 +213,9 @@ def _single_tensor_adafactor(
         exp_avg_sq = exp_avg_sqs[i]
         exp_avg = exp_avgs[i]
         step_t = state_steps[i]
+        if eps is None:
+            # use square of machine eps for grad dtype if not set
+            eps = torch.finfo(grad.dtype).eps ** 2
 
         # Update step
         step_t += 1
@@ -219,6 +223,7 @@ def _single_tensor_adafactor(
         one_minus_beta2_t = 1 - beta2_t
 
         grad_sqr = torch.square(grad) + eps
+        # NOTE application of eps (epsilon1) mirrors the optax/big vision/t5x approach
         if exp_avg_sq is None:
             # factorized second moment
             d1, d0 = _factored_dims(grad.shape, True, min_dim_size_to_factor=min_dim_size_to_factor)