diff --git a/ggml/src/ggml-cuda/fwht.cu b/ggml/src/ggml-cuda/fwht.cu
index 184dc254c..67eea594d 100644
--- a/ggml/src/ggml-cuda/fwht.cu
+++ b/ggml/src/ggml-cuda/fwht.cu
@@ -1,9 +1,10 @@
 #include "common.cuh"
+#include "convert.cuh"
 #include "fwht.cuh"
 
-template <int N>
+template <int N, typename T>
 __launch_bounds__(4*ggml_cuda_get_physical_warp_size(), 1)
-__global__ void fwht_cuda(const float * src, float * dst, const int64_t n_rows, const float scale) {
+__global__ void fwht_cuda(const T * src, float * dst, const int64_t n_rows, const float scale) {
     constexpr int warp_size = ggml_cuda_get_physical_warp_size();
 
     const int64_t r = (int64_t) blockIdx.x * blockDim.y + threadIdx.y;
@@ -22,7 +23,7 @@ __global__ void fwht_cuda(const float * src, float * dst, const int64_t n_rows,
     ggml_cuda_pdl_sync();
 #pragma unroll
     for (int i = 0; i < el_w; ++i) {
-        reg[i] = src[i * warp_size + lane] * scale;
+        reg[i] = ggml_cuda_cast<float>(src[i * warp_size + lane]) * scale;
     }
 
 #pragma unroll
@@ -58,15 +59,12 @@ __global__ void fwht_cuda(const float * src, float * dst, const int64_t n_rows,
     }
 }
 
-bool ggml_cuda_op_fwht(ggml_backend_cuda_context & ctx, const ggml_tensor * src, ggml_tensor * dst) {
-    GGML_ASSERT(ggml_are_same_shape(src, dst));
-    if (!ggml_is_contiguous(src) || !ggml_is_contiguous(dst)) {
-        return false;
-    }
+template <typename T>
+static bool ggml_cuda_op_fwht_impl(ggml_backend_cuda_context & ctx, const ggml_tensor * src, ggml_tensor * dst) {
     const int     n    = src->ne[0];
     const int64_t rows = ggml_nrows(src);
 
-    const float * src_d = (const float *) src->data;
+    const T *     src_d = (const T *) src->data;
     float *       dst_d = (float *) dst->data;
 
     const int warp_size = ggml_cuda_info().devices[ggml_cuda_get_device()].warp_size;
@@ -84,18 +82,47 @@ bool ggml_cuda_op_fwht(ggml_backend_cuda_context & ctx, const ggml_tensor * src,
 
     switch (n) {
         case 64:
-            ggml_cuda_kernel_launch(fwht_cuda<64>, launch_params, src_d, dst_d, rows, scale);
+            ggml_cuda_kernel_launch(fwht_cuda<64, T>, launch_params, src_d, dst_d, rows, scale);
             return true;
         case 128:
-            ggml_cuda_kernel_launch(fwht_cuda<128>, launch_params, src_d, dst_d, rows, scale);
+            ggml_cuda_kernel_launch(fwht_cuda<128, T>, launch_params, src_d, dst_d, rows, scale);
             return true;
         case 256:
-            ggml_cuda_kernel_launch(fwht_cuda<256>, launch_params, src_d, dst_d, rows, scale);
+            ggml_cuda_kernel_launch(fwht_cuda<256, T>, launch_params, src_d, dst_d, rows, scale);
             return true;
         case 512:
-            ggml_cuda_kernel_launch(fwht_cuda<512>, launch_params, src_d, dst_d, rows, scale);
+            ggml_cuda_kernel_launch(fwht_cuda<512, T>, launch_params, src_d, dst_d, rows, scale);
             return true;
         default:
             return false;
     }
 }
+
+bool ggml_cuda_op_mul_mat_use_fwht(const struct ggml_tensor * op) {
+    const struct ggml_tensor * a = op->src[0];
+    const struct ggml_tensor * b = op->src[1];
+
+    return op->op == GGML_OP_MUL_MAT && ggml_get_op_params_i32(op, 1) == GGML_HINT_SRC0_IS_HADAMARD &&
+           a->type == GGML_TYPE_F32 && op->type == GGML_TYPE_F32 &&
+           (b->type == GGML_TYPE_F32 || b->type == GGML_TYPE_F16) && ggml_is_contiguous(b) && ggml_is_contiguous(op) &&
+           ggml_are_same_shape(b, op);
+}
+
+bool ggml_cuda_op_fwht(ggml_backend_cuda_context & ctx, const ggml_tensor * src, ggml_tensor * dst) {
+    GGML_ASSERT(ggml_are_same_shape(src, dst));
+    if (!ggml_is_contiguous(src) || !ggml_is_contiguous(dst)) {
+        return false;
+    }
+    if (dst->type != GGML_TYPE_F32) {
+        return false;
+    }
+
+    switch (src->type) {
+        case GGML_TYPE_F32:
+            return ggml_cuda_op_fwht_impl<float>(ctx, src, dst);
+        case GGML_TYPE_F16:
+            return ggml_cuda_op_fwht_impl<half>(ctx, src, dst);
+        default:
+            return false;
+    }
+}
diff --git a/ggml/src/ggml-cuda/fwht.cuh b/ggml/src/ggml-cuda/fwht.cuh
index cf3df94ca..e7ad53475 100644
--- a/ggml/src/ggml-cuda/fwht.cuh
+++ b/ggml/src/ggml-cuda/fwht.cuh
@@ -1,4 +1,6 @@
 #include "common.cuh"
 
+bool ggml_cuda_op_mul_mat_use_fwht(const struct ggml_tensor * op);
+
 // Returns whether the Fast Walsh-Hadamard transform could be used.
 bool ggml_cuda_op_fwht(ggml_backend_cuda_context & ctx, const ggml_tensor * src, ggml_tensor * dst);
diff --git a/ggml/src/ggml-cuda/ggml-cuda.cu b/ggml/src/ggml-cuda/ggml-cuda.cu
index e76ff3128..cf9a587f7 100644
--- a/ggml/src/ggml-cuda/ggml-cuda.cu
+++ b/ggml/src/ggml-cuda/ggml-cuda.cu
@@ -1818,8 +1818,7 @@ static bool ggml_cuda_should_fuse_mul_mat_vec_q(const ggml_tensor * tensor) {
 static void ggml_cuda_mul_mat(ggml_backend_cuda_context & ctx, const ggml_tensor * src0, const ggml_tensor * src1, ggml_tensor * dst) {
     GGML_TENSOR_BINARY_OP_LOCALS
 
-    const int32_t hint = ggml_get_op_params_i32(dst, 1);
-    if (hint == GGML_HINT_SRC0_IS_HADAMARD && ggml_cuda_op_fwht(ctx, src1, dst)) {
+    if (ggml_cuda_op_mul_mat_use_fwht(dst) && ggml_cuda_op_fwht(ctx, src1, dst)) {
         return;
     }
 
@@ -5212,7 +5211,7 @@ static bool ggml_backend_cuda_device_supports_op(ggml_backend_dev_t dev, const g
                 if (a->nb[0] != ggml_element_size(a) || b->nb[0] != ggml_element_size(b)) {
                     return false; // TODO this could in principle be implemented though currently there is no use case.
                 }
-                if (b->type == GGML_TYPE_F16 && a->type != GGML_TYPE_F16) {
+                if (b->type == GGML_TYPE_F16 && a->type != GGML_TYPE_F16 && !ggml_cuda_op_mul_mat_use_fwht(op)) {
                     return false;
                 }
                 if (op->op == GGML_OP_MUL_MAT_ID && ggml_get_op_params_i32(op, 3) == GGML_PREC_F32) {