[Flax] time embedding (#1081)

* initial get_sinusoidal_embeddings

* added asserts

* better var name

* fix docs

src/diffusers/models/embeddings_flax.py

@@ -17,23 +17,41 @@ import flax.linen as nn
 import jax.numpy as jnp
 
 
-# This is like models.embeddings.get_timestep_embedding (PyTorch) but
-# less general (only handles the case we currently need).
-def get_sinusoidal_embeddings(timesteps, embedding_dim, freq_shift: float = 1):
+def get_sinusoidal_embeddings(
+    timesteps: jnp.ndarray,
+    embedding_dim: int,
+    freq_shift: float = 1,
+    min_timescale: float = 1,
+    max_timescale: float = 1.0e4,
+    flip_sin_to_cos: bool = False,
+    scale: float = 1.0,
+) -> jnp.ndarray:
+    """Returns the positional encoding (same as Tensor2Tensor).
+    Args:
+        timesteps: a 1-D Tensor of N indices, one per batch element.
+        These may be fractional.
+        embedding_dim: The number of output channels.
+        min_timescale: The smallest time unit (should probably be 0.0).
+        max_timescale: The largest time unit.
+    Returns:
+        a Tensor of timing signals [N, num_channels]
     """
-    This matches the implementation in Denoising Diffusion Probabilistic Models: Create sinusoidal timestep embeddings.
+    assert timesteps.ndim == 1, "Timesteps should be a 1d-array"
+    assert embedding_dim % 2 == 0, f"Embedding dimension {embedding_dim} should be even"
+    num_timescales = float(embedding_dim // 2)
+    log_timescale_increment = math.log(max_timescale / min_timescale) / (num_timescales - freq_shift)
+    inv_timescales = min_timescale * jnp.exp(jnp.arange(num_timescales, dtype=jnp.float32) * -log_timescale_increment)
+    emb = jnp.expand_dims(timesteps, 1) * jnp.expand_dims(inv_timescales, 0)
 
-    :param timesteps: a 1-D tensor of N indices, one per batch element.
-                      These may be fractional.
-    :param embedding_dim: the dimension of the output. :param max_period: controls the minimum frequency of the
-    embeddings. :return: an [N x dim] tensor of positional embeddings.
-    """
-    half_dim = embedding_dim // 2
-    emb = math.log(10000) / (half_dim - freq_shift)
-    emb = jnp.exp(jnp.arange(half_dim) * -emb)
-    emb = timesteps[:, None] * emb[None, :]
-    emb = jnp.concatenate([jnp.cos(emb), jnp.sin(emb)], -1)
-    return emb
+    # scale embeddings
+    scaled_time = scale * emb
+
+    if flip_sin_to_cos:
+        signal = jnp.concatenate([jnp.cos(scaled_time), jnp.sin(scaled_time)], axis=1)
+    else:
+        signal = jnp.concatenate([jnp.sin(scaled_time), jnp.cos(scaled_time)], axis=1)
+    signal = jnp.reshape(signal, [jnp.shape(timesteps)[0], embedding_dim])
+    return signal
 
 
 class FlaxTimestepEmbedding(nn.Module):
@@ -70,4 +88,4 @@ class FlaxTimesteps(nn.Module):
 
     @nn.compact
     def __call__(self, timesteps):
-        return get_sinusoidal_embeddings(timesteps, self.dim, freq_shift=self.freq_shift)
+        return get_sinusoidal_embeddings(timesteps, embedding_dim=self.dim, freq_shift=self.freq_shift)