diff --git a/candle-nn/src/batch_norm.rs b/candle-nn/src/batch_norm.rs
new file mode 100644
index 00000000..d1aa2148
--- /dev/null
+++ b/candle-nn/src/batch_norm.rs
@@ -0,0 +1,154 @@
+//! Batch Normalization.
+//!
+//! This layer applies Batch Normalization over a mini-batch of inputs as described in [`Batch
+//! Normalization`]. The input is expected to have at least three dimensions.
+//!
+//! Note that this implementation is for inference only, there is no possibility to track the
+//! running stats.
+//!
+//! [`Batch Normalization`]: https://arxiv.org/abs/1502.03167
+use candle::{DType, Result, Tensor};
+
+#[derive(Debug, Clone, Copy, PartialEq)]
+pub struct BatchNormConfig {
+    pub eps: f64,
+    pub remove_mean: bool,
+    /// The meaning of affine here is different from LayerNorm: when false there is no learnable
+    /// parameter at all, 1 used for gamma and 0 for beta.
+    pub affine: bool,
+}
+
+impl Default for BatchNormConfig {
+    fn default() -> Self {
+        Self {
+            eps: 1e-5,
+            remove_mean: true,
+            affine: true,
+        }
+    }
+}
+
+impl From<f64> for BatchNormConfig {
+    fn from(eps: f64) -> Self {
+        Self {
+            eps,
+            remove_mean: true,
+            affine: true,
+        }
+    }
+}
+
+#[derive(Debug)]
+pub struct BatchNorm {
+    weight_and_bias: Option<(Tensor, Tensor)>,
+    remove_mean: bool,
+    eps: f64,
+    num_features: usize,
+}
+
+impl BatchNorm {
+    pub fn new(num_features: usize, weight: Tensor, bias: Tensor, eps: f64) -> Result<Self> {
+        if eps < 0. {
+            candle::bail!("batch-norm eps cannot be negative {eps}")
+        }
+        if weight.dims() != [num_features] {
+            candle::bail!(
+                "batch-norm unexpected weight shape {:?} {num_features}",
+                weight.shape()
+            )
+        }
+        if bias.dims() != [num_features] {
+            candle::bail!(
+                "batch-norm unexpected bias shape {:?} {num_features}",
+                bias.shape()
+            )
+        }
+        Ok(Self {
+            weight_and_bias: Some((weight, bias)),
+            remove_mean: true,
+            eps,
+            num_features,
+        })
+    }
+
+    pub fn new_no_bias(num_features: usize, eps: f64) -> Result<Self> {
+        if eps < 0. {
+            candle::bail!("batch-norm eps cannot be negative {eps}")
+        }
+        Ok(Self {
+            weight_and_bias: None,
+            remove_mean: true,
+            eps,
+            num_features,
+        })
+    }
+}
+
+impl crate::Module for BatchNorm {
+    fn forward(&self, x: &Tensor) -> Result<Tensor> {
+        let x_dtype = x.dtype();
+        let internal_dtype = match x_dtype {
+            DType::F16 | DType::BF16 => DType::F32,
+            d => d,
+        };
+        if x.rank() < 2 {
+            candle::bail!(
+                "batch-norm input tensor must have at least two dimensions ({:?})",
+                x.shape()
+            )
+        }
+        if x.dim(1)? != self.num_features {
+            candle::bail!(
+                "batch-norm input doesn't have the expected number of features ({:?} <> {})",
+                x.shape(),
+                self.num_features
+            )
+        }
+        let x = x.to_dtype(internal_dtype)?;
+        let x = x.transpose(0, 1)?;
+        let x_dims_post_transpose = x.dims();
+        let x = x.flatten_from(1)?.contiguous()?;
+        let x = if self.remove_mean {
+            let mean_x = x.mean_keepdim(1)?;
+            x.broadcast_sub(&mean_x)?
+        } else {
+            x
+        };
+        let norm_x = x.sqr()?.mean_keepdim(1)?;
+        let x_normed = x.broadcast_div(&(norm_x + self.eps)?.sqrt()?)?;
+        let x = x_normed.to_dtype(x_dtype)?;
+        let x = match &self.weight_and_bias {
+            None => x,
+            Some((weight, bias)) => {
+                let weight = weight.reshape((self.num_features, 1))?;
+                let bias = bias.reshape((self.num_features, 1))?;
+                x.broadcast_mul(&weight)?.broadcast_add(&bias)?
+            }
+        };
+        x.reshape(x_dims_post_transpose)?.transpose(0, 1)
+    }
+}
+
+pub fn batch_norm<C: Into<BatchNormConfig>>(
+    num_features: usize,
+    config: C,
+    vb: crate::VarBuilder,
+) -> Result<BatchNorm> {
+    let config = config.into();
+    if config.eps < 0. {
+        candle::bail!("batch-norm eps cannot be negative {}", config.eps)
+    }
+    let weight_and_bias = if config.affine {
+        let weight = vb.get_or_init(num_features, "weight", crate::Init::Const(1.))?;
+        let bias = vb.get_or_init(num_features, "bias", crate::Init::Const(0.))?;
+        Some((weight, bias))
+    } else {
+        None
+    };
+    Ok(BatchNorm {
+        weight_and_bias,
+        remove_mean: config.remove_mean,
+        eps: config.eps,
+        num_features,
+    })
+}
diff --git a/candle-nn/src/lib.rs b/candle-nn/src/lib.rs
index da63d592..7b486f71 100644
--- a/candle-nn/src/lib.rs
+++ b/candle-nn/src/lib.rs
@@ -1,6 +1,7 @@
 use candle::{Result, Tensor};
 
 pub mod activation;
+pub mod batch_norm;
 pub mod conv;
 pub mod embedding;
 pub mod group_norm;
@@ -13,6 +14,7 @@ pub mod optim;
 pub mod var_builder;
 
 pub use activation::Activation;
+pub use batch_norm::{batch_norm, BatchNorm, BatchNormConfig};
 pub use conv::{conv1d, conv2d, Conv1d, Conv1dConfig, Conv2d, Conv2dConfig};
 pub use embedding::{embedding, Embedding};
 pub use group_norm::{group_norm, GroupNorm};
diff --git a/candle-nn/tests/batch_norm.rs b/candle-nn/tests/batch_norm.rs
new file mode 100644
index 00000000..1575e914
--- /dev/null
+++ b/candle-nn/tests/batch_norm.rs
@@ -0,0 +1,70 @@
+#[cfg(feature = "mkl")]
+extern crate intel_mkl_src;
+
+mod test_utils;
+
+use anyhow::Result;
+use candle::{Device, Tensor};
+use candle_nn::{BatchNorm, Module};
+
+/* The test below has been generated using the following PyTorch code:
+import torch
+torch.manual_seed(19551105)
+m = torch.nn.BatchNorm2d(5, affine=False)
+input = torch.randn(2, 5, 3, 4)
+output = m(input)
+print(input.flatten())
+print(output.flatten())
+*/
+#[test]
+fn batch_norm() -> Result<()> {
+    let bn = BatchNorm::new_no_bias(5, 1e-8)?;
+    let input: [f32; 120] = [
+        -0.7493, -1.0410, 1.6977, -0.6579, 1.7982, -0.0087, 0.2812, -0.1190, 0.2908, -0.5975,
+        -0.0278, -0.2138, -1.3130, -1.6048, -2.2028, 0.9452, 0.4002, 0.0831, 1.0004, 0.1860,
+        0.5004, 0.5539, 0.9991, -0.2540, -0.0703, -0.3752, -0.1096, -0.2374, 1.0258, -2.2208,
+        -0.0257, 0.6073, -1.1627, -0.0964, -1.9718, 1.6577, 0.1931, -0.3692, -0.8011, 0.9059,
+        0.4797, 0.6521, -0.0165, -0.6683, -0.4148, 2.0649, -0.8276, 1.7947, -0.2061, 0.5812,
+        -1.3598, 1.6192, 1.0466, -0.4423, 0.4202, 0.1749, 0.6969, 0.2616, -0.0369, -1.4951,
+        -0.0814, -0.1877, 0.0267, 0.6150, 0.2402, -1.1440, -2.0068, 0.6032, -2.6639, 0.8260,
+        0.1085, -0.1693, 1.2805, 0.7654, -0.4930, 0.3770, 1.1309, 0.2303, 0.2949, -0.2634, -0.5225,
+        0.4269, 0.6341, 1.5736, 0.9827, -1.2499, 0.3509, -1.6243, -0.8123, 0.7634, -0.3047, 0.0143,
+        -0.4032, 0.0537, 0.7022, 0.8405, -1.2221, -1.6847, -0.0714, -0.1608, 0.5579, -1.5858,
+        0.4617, -0.6480, 0.1332, 0.0419, -0.9784, 0.4173, 1.2313, -1.9046, -0.1656, 0.1259, 0.0763,
+        1.4252, -0.9115, -0.1093, -0.3100, -0.6734, -1.4357, 0.9205,
+    ];
+    let input = Tensor::new(&input, &Device::Cpu)?.reshape((2, 5, 3, 4))?;
+    let output = bn.forward(&input)?;
+    assert_eq!(output.dims(), &[2, 5, 3, 4]);
+    let output = output.flatten_all()?;
+    assert_eq!(
+        test_utils::to_vec1_round(&output, 4)?,
+        &[
+            -0.6391, -0.9414, 1.8965, -0.5444, 2.0007, 0.1283, 0.4287, 0.014, 0.4387, -0.4818,
+            0.1085, -0.0842, -1.6809, -2.0057, -2.6714, 0.8328, 0.2262, -0.1268, 0.8943, -0.0123,
+            0.3377, 0.3973, 0.8928, -0.5021, 0.0861, -0.2324, 0.0451, -0.0884, 1.2311, -2.1603,
+            0.1327, 0.7939, -1.055, 0.0589, -1.9002, 1.8912, 0.2918, -0.3253, -0.7993, 1.0741,
+            0.6063, 0.7955, 0.0617, -0.6536, -0.3754, 2.3461, -0.8284, 2.0495, -0.201, 0.6476,
+            -1.4446, 1.7665, 1.1493, -0.4556, 0.4741, 0.2097, 0.7723, 0.3031, -0.0186, -1.5905,
+            0.053, -0.0572, 0.165, 0.7746, 0.3862, -1.0481, -1.9422, 0.7624, -2.6231, 0.9933,
+            0.2498, -0.0381, 1.2061, 0.6327, -0.7681, 0.2004, 1.0396, 0.037, 0.109, -0.5125,
+            -0.8009, 0.2559, 0.4865, 1.5324, 1.1861, -1.1461, 0.5261, -1.5372, -0.689, 0.957,
+            -0.1587, 0.1745, -0.2616, 0.2156, 0.8931, 1.0375, -1.2614, -1.7691, 0.0015, -0.0966,
+            0.6921, -1.6605, 0.5866, -0.6313, 0.226, 0.1258, -0.9939, 0.5378, 1.3484, -2.0319,
+            -0.1574, 0.1568, 0.1034, 1.5574, -0.9614, -0.0967, -0.313, -0.7047, -1.5264, 1.0134
+        ]
+    );
+    let bn2 = BatchNorm::new(
+        5,
+        Tensor::new(&[0.5f32], &Device::Cpu)?.broadcast_as(5)?,
+        Tensor::new(&[-1.5f32], &Device::Cpu)?.broadcast_as(5)?,
+        1e-8,
+    )?;
+    let output2 = bn2.forward(&input)?;
+    assert_eq!(output2.dims(), &[2, 5, 3, 4]);
+    let output2 = output2.flatten_all()?;
+    let diff2 = ((output2 - (output * 0.5)?)? + 1.5)?.sqr()?;
+    let sum_diff2 = diff2.sum_keepdim(0)?;
+    assert_eq!(test_utils::to_vec1_round(&sum_diff2, 4)?, &[0f32]);
+    Ok(())
+}