diff --git a/serket/image/__init__.py b/serket/image/__init__.py
index afb9f6f..664bd50 100644
--- a/serket/image/__init__.py
+++ b/serket/image/__init__.py
@@ -54,11 +54,11 @@
     "RandomContrast2D",
     # filter
     "AvgBlur2D",
+    "FFTAvgBlur2D",
     "FFTFilter2D",
+    "FFTGaussianBlur2D",
     "Filter2D",
     "GaussianBlur2D",
-    "FFTAvgBlur2D",
-    "FFTGaussianBlur2D",
     # geometric
     "HorizontalFlip2D",
     "HorizontalShear2D",
diff --git a/serket/image/filter.py b/serket/image/filter.py
index d6b1579..cd725c3 100644
--- a/serket/image/filter.py
+++ b/serket/image/filter.py
@@ -125,8 +125,9 @@ class AvgBlur2D(AvgBlur2DBase):
     def __call__(self, x: jax.Array) -> jax.Array:
         x = jnp.expand_dims(x, 1)
         x = jax.vmap(filter_2d, in_axes=(0, None))(x, self.kernel)
-        x = jax.vmap(filter_2d, in_axes=(0, None))(x, jnp.moveaxis(self.kernel, 2, 3))
-        x = x[:, 0]
+        k = jnp.moveaxis(self.kernel, 2, 3)
+        x = jax.vmap(filter_2d, in_axes=(0, None))(x, k)
+        x = jnp.squeeze(x, 1)
         return x
 
 
@@ -154,8 +155,9 @@ class FFTAvgBlur2D(AvgBlur2DBase):
     @ft.partial(validate_spatial_ndim, attribute_name="spatial_ndim")
     def __call__(self, x: jax.Array) -> jax.Array:
         x = jnp.expand_dims(x, 1)
-        x = jax.vmap(filter_2d, in_axes=(0, None))(x, self.kernel)
-        x = jax.vmap(filter_2d, in_axes=(0, None))(x, jnp.moveaxis(self.kernel, 2, 3))
+        x = jax.vmap(fft_filter_2d, in_axes=(0, None))(x, self.kernel)
+        k = jnp.moveaxis(self.kernel, 2, 3)
+        x = jax.vmap(fft_filter_2d, in_axes=(0, None))(x, k)
         x = jnp.squeeze(x, 1)
         return x
 
@@ -170,8 +172,9 @@ def __init__(
     ):
         self.kernel_size = positive_int_cb(kernel_size)
         self.sigma = sigma
-        x = jnp.linspace(-(kernel_size - 1) / 2.0, (kernel_size - 1) / 2.0, kernel_size)
-        kernel = jnp.exp(-0.5 * jnp.square(x) * jax.lax.rsqrt(self.sigma))
+        x = jnp.arange(kernel_size) - kernel_size // 2
+        x = x + 0.5 if kernel_size % 2 == 0 else x
+        kernel = jnp.exp(-(x**2) / (2 * sigma**2))
         kernel = kernel / jnp.sum(kernel)
         self.kernel = kernel[None, None, None].astype(dtype)
 
@@ -206,7 +209,8 @@ class GaussianBlur2D(GaussianBlur2DBase):
     def __call__(self, x: jax.Array) -> jax.Array:
         x = jnp.expand_dims(x, 1)
         x = jax.vmap(filter_2d, in_axes=(0, None))(x, self.kernel)
-        x = jax.vmap(filter_2d, in_axes=(0, None))(x, jnp.moveaxis(self.kernel, 2, 3))
+        k = jnp.moveaxis(self.kernel, 2, 3)
+        x = jax.vmap(filter_2d, in_axes=(0, None))(x, k)
         x = jnp.squeeze(x, 1)
         return x
 
@@ -236,8 +240,9 @@ class FFTGaussianBlur2D(GaussianBlur2DBase):
     @ft.partial(validate_spatial_ndim, attribute_name="spatial_ndim")
     def __call__(self, x: jax.Array) -> jax.Array:
         x = jnp.expand_dims(x, 1)
-        x = jax.vmap(filter_2d, in_axes=(0, None))(x, self.kernel)
-        x = jax.vmap(filter_2d, in_axes=(0, None))(x, jnp.moveaxis(self.kernel, 2, 3))
+        x = jax.vmap(fft_filter_2d, in_axes=(0, None))(x, self.kernel)
+        k = jnp.moveaxis(self.kernel, 2, 3)
+        x = jax.vmap(fft_filter_2d, in_axes=(0, None))(x, k)
         x = jnp.squeeze(x, 1)
         return x
 
@@ -306,12 +311,7 @@ class FFTFilter2D(sk.TreeClass):
           [4.        6.0000005 6.0000005 6.0000005 4.       ]]]
     """
 
-    def __init__(
-        self,
-        kernel: jax.Array,
-        *,
-        dtype: DType = jnp.float32,
-    ):
+    def __init__(self, kernel: jax.Array, *, dtype: DType = jnp.float32):
         if kernel.ndim != 2:
             raise ValueError("Expected `kernel` to be a 2D `ndarray` with shape (H, W)")
 
@@ -320,7 +320,7 @@ def __init__(
     @ft.partial(validate_spatial_ndim, attribute_name="spatial_ndim")
     def __call__(self, x: jax.Array) -> jax.Array:
         x = jnp.expand_dims(x, 1)
-        x = jax.vmap(filter_2d, in_axes=(0, None))(x, self.kernel)
+        x = jax.vmap(fft_filter_2d, in_axes=(0, None))(x, self.kernel)
         x = jnp.squeeze(x, 1)
         return x