diff --git a/candle-core/src/cpu_backend.rs b/candle-core/src/cpu_backend.rs
index 05c1f4e8..0ec19559 100644
--- a/candle-core/src/cpu_backend.rs
+++ b/candle-core/src/cpu_backend.rs
@@ -1060,7 +1060,6 @@ impl<'a> Map2 for Conv2D<'a> {
                         let dst_idx = dst_idx + dst_w;
                         let mut d = T::zero();
                         for offset_h in 0..p.k_h {
-                            // TODO: Handle the case where padding is larger than p.k_h / 2.
                             let src_h = (p.stride * dst_h + offset_h)
                                 .saturating_sub(p.padding)
                                 .min(p.i_h - 1);
diff --git a/candle-core/tests/conv_tests.rs b/candle-core/tests/conv_tests.rs
index 4ef47780..7ec83592 100644
--- a/candle-core/tests/conv_tests.rs
+++ b/candle-core/tests/conv_tests.rs
@@ -39,6 +39,37 @@ fn conv1d() -> Result<()> {
         test_utils::to_vec1_round(&res.flatten_all()?, 4)?,
         [2.6357, -1.3336, 4.1393, -1.1784, 3.5675, 0.5069]
     );
+    let res = t.conv1d(&w, /*padding*/ 1, 1)?;
+    assert_eq!(res.dims(), [1, 2, 5]);
+    /* Note that the default for padding is different from PyTorch at the moment: instead of
+       padding with zeros, the edge value from the input tensor is used, i.e. this is similiar to:
+    t = torch.nn.functional.pad(t, (1, 1), mode='replicate')
+    res = torch.nn.functional.conv1d(t, w, padding=0)
+    */
+    assert_eq!(
+        test_utils::to_vec1_round(&res.flatten_all()?, 4)?,
+        [2.5209, 2.6357, -1.3336, 4.1393, 0.4951, 3.6855, -1.1784, 3.5675, 0.5069, 4.9562]
+    );
+    Ok(())
+}
+
+#[test]
+fn conv1d_small() -> Result<()> {
+    let dev = &Device::Cpu;
+    let t = Tensor::new(&[0.4056f32, -0.8689, -0.0773, -1.5630], dev)?.reshape((1, 1, 4))?;
+    let w = Tensor::new(&[1f32, 0., 0.], dev)?.reshape((1, 1, 3))?;
+    let res = t.conv1d(&w, 0, 1)?;
+    assert_eq!(res.dims(), [1, 1, 2]);
+    assert_eq!(
+        test_utils::to_vec1_round(&res.flatten_all()?, 4)?,
+        [0.4056, -0.8689]
+    );
+    let res = t.conv1d(&w, /*padding*/ 1, 1)?;
+    assert_eq!(res.dims(), [1, 1, 4]);
+    assert_eq!(
+        test_utils::to_vec1_round(&res.flatten_all()?, 4)?,
+        [0.4056, 0.4056, -0.8689, -0.0773],
+    );
     Ok(())
 }